“It’s a game of football. You have had two grown men basically square up, no punches have been thrown, nothing serious has happened, both have gone home to their families, one team has lost, one team has won.
“We have to be careful not to get too carried away. We have to remember what makes football football.
“It’s that kind of thing, it’s goals, it’s playing on the edge, it’s high intensity, it’s high passion. That’s why we do what we do, that’s why we love watching football.”
The Spaniard was sent off following the clash with the Everton midfielder in the 84th minute at Goodison Park.
A Chelsea spokesman said: “Diego spoke to club officials and expressed regret over his reaction to the challenge from Barry that led to his red card.
“But Diego was also very clear that he did not bite him at any point during that altercation.”
Chelsea manager Guus Hiddink claims Everton deliberately provoked Costa, who had a running battle with Barry throughout the tie.
In the incident that led to Costa’s second yellow card, the 27-year-old confronted Barry, moving his head towards him and in the direction of his neck.
“He was chased a bit in the game by Everton. They went after him. They knew it. It is within the rules,” said Hiddink.
“As a referee you have to protect the situation, but knowing and feeling this atmosphere.”
Hiddink, who managed Chelsea to victory over Everton in the 2009 FA Cup final, said he had not seen the incident that led to Costa’s dismissal.
“I try to be fair in my judgement and it is difficult for me to say yes or no so I don’t want to give judgement on this,” he said.
Everton manager Roberto Martinez said midfielder Barry, 35, had not complained about the incident – and was more interested in a win that takes his side to a semi-final at Wembley rather than any incident involving Costa.
Martinez said: “My interpretation is I don’t think it was a key moment. It was an emotional game and rightly so.
“Diego Costa has a fighting spirit and I would like to praise the referee. The sending off of Diego Costa was right as I thought it was a second yellow card and the sending off of Gareth Barry was right.
“After we have won a game like this and got to Wembley, which our fans deserve so much, the last thing I am going to do is see if an opposing player has bit my player. Gareth Barry has said it is nothing to worry about. He is just disappointed he got a second yellow card.”
It was Costa’s first sending off since he joined Chelsea in summer 2014, although he received a retrospective three-game ban in January 2015 for stamping on Liverpool’s Emre Can in a League Cup semi-final at Stamford Bridge.
Hiddink was asked whether Chelsea had considered an anger management cause for the confrontational Spain striker and joked: “There are movies about that, aren’t there? Wasn’t Jack Nicholson in a film called Anger Management? Maybe we can go and watch it together.”
Will Costa face retrospective punishment?
Former Premier League referee Howard Webb told BBC Radio 5 live: “I’ve watched the incident back and I am pretty confident that [referee] Michael Oliver has shown Costa a second yellow card for adopting an aggressive attitude.
“There is no way Michael Oliver can see what happens then with the neck – if it is a bite or not. He couldn’t see it anyway as he is looking at the other side of Gareth Barry.
“Two things I think will happen now. I think the FA will look at the footage so they can try and see if a bite has taken place.
“They will look for evidence, for Gareth Barry’s reaction, for marks on the neck. They will then come to a judgement and that will go down as something unseen by Michael Oliver.
“Secondly, I’ll be amazed if Costa is not punished for his reaction after the second yellow card. He fails to leave the field of play, he is aggressive again to Michael Oliver and referees are always told to report that situation. That can lead to another match ban.
“The only time you could be sent off for attempting to bite is if you make the action to bite and the other player pulls away.
“But it looks like he has thought about it but not gone through with it. From what I’ve seen of the footage, it is not sufficient to support a charge for violent conduct retrospectively.”
They remain unbeaten in the Premier League since he took charge but I still don’t think Chelsea have really clicked under Hiddink, who has the job until the end of the season.
They have not been fluent for some reason and it was the same when I saw them lose to Everton at Goodison Park on Saturday. They were not good enough.
I look through Chelsea’s squad and think they should be a great team but, even when they win under Hiddink, they are still a little mechanical and are missing a bit of flair.
I think this is why the board wants to try something different with their next manager, which is the main reason they have not given the job to Guus permanently. I think he wanted it, because he loves life in London.
Hiddink denied another fairytale finish
I played briefly under Guus when I was a young player – and when he was a young coach – starting out at PSV Eindhoven in 1987. We get along very well. Since then he has developed his way of coaching and he has had a great career.
There have been ups and downs, of course, and he has not had a great time since his last spell at Chelsea when he won the FA Cup in 2009, but anyone who has spent as long as he has in the game would be the same.
His strengths are that he is an excellent man-manager. The main thing with him is that he knows how to deal with good players, to motivate them and make them feel right.
Tactically he is versatile. He plays on the strengths of the players he has got, which is why he has done a good job since coming back to Stamford Bridge to take Chelsea up the Premier League table.
Jose Mourinho’s teams always play the same way but I would not look at a Hiddink side and say that. His style is far more adaptable.
At Chelsea, it had been working pretty well until this week, when I felt they lacked aggression going forward against Paris Saint-Germain on Wednesday.
If you don’t put your opponents under pressure then they get more and more confident, which is exactly what happened at Stamford Bridge.
Going out of the Champions League meant the FA Cup was very important to Hiddink – he would obviously have loved to have signed off with another Wembley win.
Instead, Romelu Lukaku’s goals mean Chelsea must look ahead to next season – and how they can improve.
What next: Conte in, Terry out?
It was a surprise to see Antonio Conte linked with the Chelsea job – and until he is appointed nothing is definite – but the newspapers say the Italy boss is the big favourite to take over after Euro 2016.
If it is Conte, his first job will be to get Chelsea back into the Champions League, because that will be a big miss for the club next season. It will not be easy.
Last time Hiddink was in temporary charge, in 2009, Carlo Ancelotti came in next and did a great job.
Ancelotti won the Double in his first season but things were a bit different then – the Chelsea squad looked more balanced and had more quality, and the likes of Petr Cech, John Terry, Frank Lampard and Didier Drogba were at the very top of their game.
This time, the new manager will also have some fantastic players but there are some question marks over what the future holds for the likes of Hazard, Costa and Terry – in his case, because of his age.
I said at the start of the season that I thought Terry was still Chelsea’s most important player because a good foundation is the most important thing for any team.
We have seen that is true because of the way they struggled when he was out of sorts earlier in the season.
So I am curious about what will happen with Terry next, and whether he will get a new contract.
I understand he is 35 but he has a very important impact not just on the pitch but also in the dressing room and as a link to the fans. Surely he still has a part to play.
Ruud Gullit was speaking to BBC Sport’s Chris Bevan.