Liverpool: The Liverpool manager Klopp could be seen exchanging words with a fan standing behind the dug-outs after a first-half back-pass towards goalkeeper Simon Mignolet was met by a collective groan around Anfield.
Klopp said his side were committed to building play from the back and asked supporters not to allow their impatience to get the better of them.
"If we don't play possession football tonight, it's ping-pong," Klopp told reporters after Tuesday's game.
"We played high pressure, so Chelsea does it smart, plays a few long balls. If we do the same, you have a stiff neck after the game.
"So we had to play football and that includes sometimes you play a back-pass. And then I hear in this moment (shouts): 'Why you play a back-pass?'
"Keep your nerve, please. It's still football. I have no problem with emotion. I have much more emotions than I should have. But it's in this moment (I think), 'What do you want?'
"It was only one guy, by the way, that I made eye contact with. Blue jacket."
The draw preserved the 10-point gap separating the sides, but meant Liverpool, who remain fourth, avoided four successive home defeats for the first time since 1923.
Chelsea took a 24th-minute lead when David Luiz's quickly taken free-kick caught out Mignolet as he tried to organise his defence, the ball cannoning in off his right-hand post.
Georginio Wijnaldum equalised with a 57th-minute header before Mignolet atoned by saving a penalty from Diego Costa, awarded for a foul on the Chelsea striker by Joel Matip.
Klopp celebrated Mignolet's penalty save by roaring in the face of the fourth official Neil Swarbrick, but said the pair had later made peace.
Arsenal next for Chelsea
"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.'"
Liverpool's supporters felt Costa went down too easily after being caught by Matip, but Klopp said he had no qualms with the combative Chelsea striker.
"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.
"What (Antonio) Conte is doing with Chelsea is outstanding, but Chelsea without Costa this season?
"He is not the nicest guy on the pitch, but I saw no real big incident.
"If someone tells me it was a dive, maybe I will be angry tomorrow, but that would be wrong decision what, number 27? But it doesn't make it better."
Despite Costa's squandered penalty, Arsenal's loss to Watford and Tottenham Hotspur's goalless draw at struggling Sunderland made it a good night for Chelsea manager Antonio Conte.
"It is not easy to play against Liverpool in this moment after three defeats. It is not easy to play in this atmosphere," said Conte, whose side sit nine points clear ahead of Arsenal's visit on Saturday.
"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.
"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."
Published Date: Feb 01, 2017 13:24 PM | Updated Date: Feb 01, 2017 13:24 PM