A header from Ibrahima Konate and then a brace from Sadio Mane put the Reds 3-0 up after 45 minutes, punishing any mistakes from their opponents in ruthless fashion.
Jack Grealish and Bernardo Silva got on the scoresheet as City threatened an incredible comeback, but finished 3-2, with all the damage done in the first half.
It should be a historic end to the season for Liverpool, who are still aiming for a quadruple, and Klopp hailed his side for the way they dismantled City early on.
“I’m absolutely proud,” said the Liverpool boss. “It’s amazing, I think the first half was one of the best we’ve ever played. We did everything right, I loved every second of it.
“The second half started with a Man City goal and then the game opened up. City’s quality is insane.
“We had counterattacks that we didn’t use and we can close the game there. It’s so hard to win against them, but because we have my boys in the dressing room, we have a chance.
Over the past week, Klopp has slammed BT Sport for its scheduling of Liverpool’s game against Newcastle, which is an early kick-off on April 30. It comes less than 72 hours after the Reds were in Champions League action against Villarreal.
As Liverpool continue to fight on all fronts, further disruption seems inevitable, which Klopp admits he just has to accept.
“We’ll have another game midweek because they have to move another one,” Klopp said.
“I don’t know if we have a full week before the last day. Everything is difficult, but who cares?
“We were aware of these issues, but we wanted to go to the final and beating the best football team in the world is quite a special moment.”