Second-half goals from Mohamed Salah and Roberto Firmino killed off any hopes of a City fightback after an early Gabriel Jesus strike, securing a 2-1 victory and a 5-1 aggregate success.
Premier League leaders City completely dominated the first half as they attempted to salvage the tie after last week’s 3-0 loss at Anfield.
Jesus’s second-minute effort electrified the crowd before Bernardo Silva hit the woodwork and Leroy Sane had a goal wrongly disallowed for offside. That sparked angry protests from City and manager Guardiola was sent to the stand for his reaction after the half-time whistle.
City could not match their first-half intensity after the break and Liverpool professionally closed out a place in the semi-finals of Europe’s elite competition for a 10th time.
Liverpool manager Jurgen Klopp rued his side’s poor start, but credited the way they came back.
“It was difficult tonight, especially with the start, this wonderful goal we served them almost on a plate,” said Klopp.
“We needed to react in the right way, I liked the reaction immediately after that.
“As normal City took all the risks they could take and we needed a little bit of luck.”
Klopp admitted that the luck came as City failed to add to their first goal.
He said: “They could have scored two or three in the first half. It was 100 per cent clear if we won a ball we would have opportunities.
“If they want the ball from you they have to kill you. We are in the semis so we deserve it.”
City boss Guardiola confirmed his dismissal was for his complaints to the referee. “I said he was wrong,” he said. “That is why he sent me off. I didn’t insult him. I said it was a penalty and the ball came off Milner.”
Roma secured a dramatic 3-0 victory over Barcelona at the Stadio Olimpico to book their place in the Champions League semi-finals on away goals after a 4-4 aggregate result.
Trailing 4-1 after the first leg, Roma went ahead on the night after six minutes through Edin Dzeko, Daniele de Rossi doubled their lead with a penalty and Kostas Manolas headed in late on.