Man City scored inside 2 minutes but that was as good as it got as the reds added two more goals to the 3 scored in the first leg.
Mo Salah and Roberto Firmino scored the goals as Man City badly faded after their first half efforts.
Liverpool join Roma in the semi final draw after Philippe Coutinho's new team Barcelona were also knocked out on the evening.
Here are the highlights from the game which was covered by BT Sport.
