Liverpool were on course to secure Champions League football – on offer to the winners of the competition this year – when Daniel Sturridge’s magnificent strike with the outside of his left foot gave them the interval lead.
But the Reds conceded three goals in the space of 24 second-half minutes – Kevin Gameiro netting 17 seconds after the interval, before Coke struck twice.
“There is no criticism and I have spoken to my players,” added Klopp.
“What I think about not being in the Champions League is that we have to use the time.
“It is not about the size of the squad, it is about using the time in training to get better.”
‘Experience was key’
Former Liverpool defender Mark Lawrenson was frustrated by the Reds’ second-half collapse.
“Experience was key after conceding,” said the 1984 European Cup winner, who was part of BBC Radio 5 live’s team in Basel.
“Where was the central defender or captain saying ‘circle the wagons for 20 minutes – we do not concede and we get ourselves back into game’? That is something Liverpool just didn’t do.
“They had one stonewall penalty in the first half but when you go in 1-0 up at half-time in a cup final, what is the first thing anyone says in the dressing room?
“You make sure you don’t concede in the first 10 or 20 minutes. What did Liverpool do? They conceded in the first 17 seconds.”
‘I’ve lost count of Moreno’s mistakes’
Left-back Alberto Moreno was at fault for Sevilla’s first goal, and Lawrenson was also critical of the 23-year-old’s performance.
“Yet again Moreno, who used to play for Sevilla, has made a massive mistake,” he said.
“I’ve lost count of how many mistakes this guy has made.
“It’s all very good pouring forward but the clue is in the title – left-back. Try defending occasionally. Moreno has made mistakes all season – basic errors.
“Where was he for Villarreal’s goal the other week? He was trying to score a goal at the other end.”
Lawrenson said former Liverpool boss Brendan Rodgers, who was sacked in October, had to share the blame for not strengthening the left-back area during his tenure.
He added: “Liverpool didn’t have, by the end of August, another player who could play left-back unless they moved Nathaniel Clyne from the right.
“Jose Enrique was never going to play. I’m sorry, Brendan Rodgers gets the blame for me.”
‘Sturridge going nowhere – except on holiday’
Lawrenson expects a summer of change at Anfield, but expects Sturridge and Brazilian duo Roberto Firmino and Philippe Coutinho to stay.
“I’d imagine Liverpool have spoken to agents and will have an indication of whether players are coming,” he said.
“If you are in a room with Klopp then I’d think it was hard to say no to him. This summer’s transfer window is going to be the biggest ever in the Premier League in terms of money spent.
“Firmino, Coutinho and Sturridge are not going anywhere this summer – other than on holiday.
“Klopp knew within two weeks of taking over he needed to bring in players.
“Why didn’t he address it in January? He probably did but could not get the right personnel in.”
A tribute to Jimmy Hill, who passed away in December 2015 having made a remarkable impact on football and football culture. His career was unique, taking in virtually every role in the sport, from the pitch to the dugout, the boardroom to the television studio.
After retiring from playing, Hill became manager of Coventry City where he pioneered new ways of developing the club’s image and its relationship with fans. He was similarly forward-thinking when he moved into influential roles in broadcasting and went on to become an iconic and long-running presenter of Match of the Day.
But perhaps Hill’s greatest legacy was his successful campaign to abolish the maximum wage, revolutionising the careers and prospects of footballers in the early 1960s and paving the way for the multimillionaire global stars of today.
The programme features contributions from former footballers, managers, broadcasters and Hill’s family.
This is a live BBC One stream starting at 22:45 BST.
Liverpool suffered a dramatic second-half collapse as Sevilla claimed the Europa League for the third season in succession with a superb comeback.
Jurgen Klopp’s side looked on course to secure the prize of Champions League football – on offer to the winners of the competition – when Daniel Sturridge’s magnificent strike with the outside of his left foot gave them the interval lead.
The good work was wrecked in the first 17 seconds of the second half when Kevin Gameiro turned in Mariano Ferreira’s cross to put Sevilla level.
Liverpool, who were denied a clear first-half penalty when Sevilla’s Daniel Carrico clearly handled as Roberto Firmino tried to weave past him, never recovered.
Coke’s fine 64th-minute finish confirmed Sevilla’s superiority and he added a contentious third from close range, which was initially disallowed but was then given as Liverpool slumped to their second final defeat this season after losing to Manchester City in the Capital One Cup.
Klopp has revived Liverpool for much of this season – indeed some of their fans were still hoping for the sort of comeback that saw them score three goals in the last 20 minutes to beat Borussia Dortmund in the quarter-final – but this defeat is a major setback to his summer strategy.
Liverpool had so much riding on this game. The lure of Champions League football, set alongside the chance to play for Klopp and at Anfield, would have completed an attractive package to set before any potential signings.
Now they cannot offer any sort of European football as they ended well beaten here in another night of disappointment for Klopp, who has now lost five successive finals with Dortmund and Liverpool.
Liverpool will still attract players of high class, but a crucial plank in their transfer strategy has been removed by this defeat.
Liverpool’s weakness exposed
Klopp’s spirit of renewal papered over some of the cracks in the Liverpool squad he inherited but they were brutally exposed by Sevilla’s second half masterclass.
Liverpool were fragile mentally after the equaliser and it was quite simply too easy to get behind their defensive unit, with Alberto Moreno’s shocking performance demonstrating once again he is a weakness that must be addressed.
Klopp’s problems were compounded by the failure of his creative players to put their stamp on the game. Philippe Coutinho barely had the ball while Firmino was subdued and substituted.
Sturridge shows his class
In one moment on 35 minutes, Sturridge showed the class that demonstrates how much he means to Liverpool and he may yet mean to England at Euro 2016.
Taking the ball on the angle of the penalty area, he produced a moment of instinctive genius, curling a left-foot finish past Sevilla keeper David Soria into the corner.
Sturridge is arguably England’s most gifted striker but has been overtaken by Harry Kane and Jamie Vardy while he has suffered injuries.
If he stays fit, England manager Roy Hodgson will have a serious dilemma at Euro 2016. Will Sturridge yet put captain Wayne Rooney under pressure for his place in France?
Liverpool’s rough luck
The better side won this Europa League final. Once they got on terms, Sevilla were simply in a different class, but how different it might have been had that penalty been given when Carrico handled under pressure from Firmino, along with one or two other acceptable claims.
Liverpool could point to those but ultimately they ended a beaten and bedraggled side, a Europa League that promised so much ended in anti-climax and disappointment.
The stats you need to know
Sevilla have won five of the past 11 Uefa Cup/Europa League campaigns.
Daniel Sturridge has scored six times in his past nine starts for Liverpool in all competitions.
Kevin Gameiro has scored seven goals in his past six Europa League games.
Coke scored his first two Europa League goals after 24 games without one.
English teams have lost three of their past four Uefa Cup/Europa League finals (Middlesbrough in 2006, Fulham in 2010 and Liverpool in 2016. Chelsea won in 2013).
Daniel Carrico and Vitolo have been in the starting line-up in each of Sevilla’s past three Europa League finals (2014, 2015 and 2016).
What they said
Liverpool captain James Milner: “We never started in the second half and it is devastating. We didn’t show anywhere near our ability and that is the biggest disappointment.
“We were ready, we made sure we said the right things at half-time. We gave a sloppy goal away and never got back into the game.
“The lineman’s flag went up for the third goal but the referee gave it the other way. It is nothing to do with the referee, it is about us. We didn’t do it on the night that mattered.
“We didn’t think about the Champions League, it was about winning this trophy. We didn’t manage to get over the line. It is a double blow not to be in Europe next season. We got into two finals and lost both, next time we need to finish the job.“
Sevilla defender Daniel Carrico: “It is three seasons in a row now and it is our competition. We have won and our star Antonio Puerta is up there, he is helping us.
“Liverpool played a good first half but the manager told us we need to change the game, we needed to believe and we did what he said. Scoring easily in the second half helped us and Liverpool did not have any chances.
“Next season we will be in the Champions League and it is another challenge for us. We will see what happens next season but it is now time to celebrate.”
Match ends, Liverpool 1, Sevilla 3.
Second Half ends, Liverpool 1, Sevilla 3.
Attempt blocked. Vicente Iborra (Sevilla) right footed shot from outside the box is blocked. Assisted by Sergio Escudero.
Nathaniel Clyne (Liverpool) is shown the yellow card for a bad foul.
Foul by Nathaniel Clyne (Liverpool).
Vitolo (Sevilla) wins a free kick in the attacking half.