The Spain international won a penalty, subsequently saved by Simon Mignolet, slightly theatrically and generally antagonised those at Anfield throughout Tuesday’s 1-1 draw with the type of performance which has seen him criticised in the past for going to ground easily.
However, Costa also caused Liverpool enough problems for Klopp to acknowledge his qualities.
“If I had played against Costa I could never be friends, that’s how it is, but when you have him in your team it’s much more fun. He is a warrior,” said Klopp.
“He is not the nicest guy on the pitch but I saw no real big incident and until someone tells me something…
“If someone tells me it was a dive maybe I will be angry tomorrow but that would be the wrong decision what, number 27, but it doesn’t make it better.”
Klopp was furious with the award of a penalty after Costa tangled with Joel Matip and took out his frustration on the fourth official.
However, after Mignolet came to Liverpool’s rescue the Reds boss calmed down sufficiently to make an apology to Neil Swarbrick in the technical area.
“It was a foul before in my opinion on (Dejan) Lovren, that’s what I was a little angry about,” Klopp said.
“No-one can beat us, was what I said (to Swarbrick). Obviously that’s not true but it felt for us like this in that moment.
“I was absolutely the wrong person to say it. I said sorry – I was a bit excited. He said ‘No problem I like your passion’.”
That passion was reflected around Anfield as the crowd responded to a performance Klopp had promised them after three successive home defeats, which included two cup exits.
“I am happy about the performance. I thought we did well from first second we were in game, we were aggressive,” he said. ”
The red shirts had passion, readiness, greed, against experience and coolness and that’s difficult.”
Klopp refused to criticise Mignolet for Chelsea‘s goal, scored from a quickly-taken free-kick by David Luiz while Liverpool’s goalkeeper was looking the other way, which was cancelled out in the second half by Georginio Wijnaldum.
“It was really smart, really clever and really well done – we have to respect that,” he said.
Despite their missed penalty Chelsea head coach Antonio Conte was happy to leave Anfield with a point, especially after learning Saturday’s opponents Arsenal lost to Watford and Tottenham were held to a goalless draw by struggling Sunderland.
“It is not easy to play against Liverpool in this moment after three defeats. It is not easy to play in this atmosphere,” he said.
“I am very proud of my players for the personality they showed tonight. It is a good point, for sure.
“When you have a good chance with a penalty in the 76th minute then you think you could win and take three points but Mignolet made a great save.
“We had two chances to score the second goal but it didn’t happen but we must be pleased.
“It wasn’t easy to play with the same intensity of Liverpool so we must be pleased.
“Now it is important to recover well as we wasted a lot of energy because the game was intense and there were a lot of mistakes.
“These high-intensity games it is very difficult to see mistakes and try to make corrections but I think today we played a really good game.”