Liverpool took a 3-0 lead to the Etihad Stadium but they had their nerves tested to the maximum early on when Gabriel Jesus netted after just 123 seconds.
Pep Guardiola was sent off at half-time for remonstrating with the referee after Leroy Sane incorrectly had a goal disallowed for offside.
Mohamed Salah and Roberto Firmino then scored in the second half to ensure Jurgen Klopp’s side progressed to the semi-finals.
However, Guardiola’s decision to name a forward-thinking line-up eventually proved costly as they were twice hit on the break to crush their European dream.
And Klopp explained after the match that he was rubbing his hands when he found out his rivals had left themselves with only three defenders at the back.
“He took all the risks and it was his decision,” Klopp told BT Sport.
“It could have been the absolute right decision.
“I know after the game it is easy to say it is the wrong decision but they could have scored two or three goals in the first half.”
Klopp also moved to praise his side’s performance and abstained his players from any criticism.
“It was quite difficult tonight,” he added.
“Again it was clear especially with the start.
“This wonderful goal were served them on a plate but I expected something like that.
“We needed to react in the right way and I liked the reaction immediately after that but didn’t play enough football.
“We needed a little bit of luck and a really disciplined defensive formation.
“I have nothing to criticise because I knew it would be difficult.”
Meanwhile, Guardiola was furious with his dismissal as he revealed what he said to the referee.
“I said it was ‘a goal’ at half time. That’s why he sent me off,” Guardiola said.
“It’s different to go to half-time 1-0 not 2-0, it’s different when Salah’s first goal at Anfield is offside.
“These are the things that influence things. Big congratulations to Liverpool, top team top manager.
“It is what it is. Congratulations to my players, and we will come back stronger next season. We now try to close the Premier League.
“I didn’t insult the referee, I just said ‘it’s a goal, it came off Milner!’
