City went into the game unbeaten after 22 league games but saw their run ended with Alex Oxlade-Chamberlain, Roberto Firmino, Mohamed Salah and Sadio Mane all scoring for Liverpool.
Leroy Sane, Bernardo Silva and Ilkay Gundogan were all in target for City.
City still top the league table on 62 points, 15 points ahead of Manchester United in second place, while Liverpool are now third on 47 points.
“You can watch it as a manager or as a football fan and I prefer to do that – wow! What a game! Two teams, full throttle,” Klopp said in his post-match interview.
“This was a historical game you will talk about in 20 years because it looks like City will not lose another one this year.
“People watched this game all over the world and this is why – take your heart, throw it on the pitch and play like this, both teams.
“We played, I don’t know which level, caused them problems like hell. I was not scared at the end, not that I didn’t think we could concede a fourth, I have known my boys long enough now, it was so intense.
“If you combine quality with attitude you see a game like this. I really loved it.
“You will find someone who wants to talk about defending, no clean sheet, but he can blow up my boots.”