Klopp was so enthralled by his side's 4-3 win and the manner of it that he was moved to drop an F-bomb live on US television.
"You can look at this game in a few different ways," said Klopp on US TV. "As a manager, you can say we could have done this and that better or you can look at it as a football fan and say what the f*** was that?"
Liverpool's German manager then jokingly added: "Oh, I thought in America it's OK. In England, it's not possible."
Liverpool had taken an early lead through Alex Oxlade-Chamberlain before Leroy Sane's powerful shot, just before half-time, pulled City level. But three stunning goals in nine minutes, from Roberto Firmino, Sadio Mane and Mohamed Salah, put Klopp's team 4-1 up.
However, Liverpool have a habit of conceding three-goal leads -- they did so in the 3-3 Champions League draw with Sevilla earlier this season -- and late goals from Bernardo Silva and Ilkay Gundogan ensured a tense finish.
"Congratulations to Liverpool for the victory," said City manager Guardiola, whose team still hold a 15-point lead over nearest rivals Manchester United in the Premier League table.
"The game was in our hands at 1-1 but our finishing was not good and then it went suddenly to 4-1.
"You have to be stable when you concede a goal and we were not solid enough. You have to live this kind of situation in the season.
"The reality is we lose the game, we have a week to recover and prepare for the Newcastle game. All credit to the opponent, we know how difficult it is against a Jurgen Klopp team, so aggressive, at Anfield too. We did a good performance, apart from a few minutes."
'Blow up my boots
The goals from Mane and Salah were a direct result of Liverpool's high press; breathless, all-action counter-attacking, dubbed gengenpressing during Klopp's time in Germany with Borussia Dortmund and Mainz.
"This was a historical game you will talk about in 20 years because it looks like City will not lose another one this year," Klopp told reporters.
"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."
The win pushed Liverpool up to third and also proved plenty of evidence that the Merseysiders remain competitive despite selling Philippe Coutinho to Barcelona.
Meanwhile, the "Invincible"
accolade that City had been chasing still can only be applied to Arsene Wenger's unbeaten Arsenal team of the 2003/04 season.