Klopp’s side kept alive their bid to win all four major trophies in a single seasons thanks to Ibrahima Konate’s opener and Sadio Mane’s double at Wembley.
Liverpool were three goals up by half-time as they tore City apart with a scintillating display that Klopp rated among the very finest of his reign.
City hit back with second half goals from Jack Grealish and Bernardo Silva, but it wasn’t enough to stop the Reds reaching their first FA Cup final since 2012.
“Absolutely proud, incredible. The first half was one of the best we ever played. We did all the right stuff, we scored in the right moments. We were outstanding. I loved each second of it,” Klopp said.
“The second half started with the goal for Man City and then it opens up. The quality of City is insane.
“We respect City so much and it’s so difficult to win against them. But because we have these boys in our dressing room we have a chance.”
Liverpool are embroiled in a fierce title fight with City, who are one point clear of Klopp’s men at the top of the Premier League with seven games left.
They shared a pulsating 2-2 draw in Manchester in the league last weekend, and could still meet in the Champions League final.
Asked if their FA Cup semi-final success could be the springboard to pip City in both the Premier League and Champions League, Klopp said: “It’s not a statement, we are just in the final.
“I think City knew beforehand that it could be difficult against us, that’s how it has been between us most of the time.”
While Liverpool are a step closer to football immortality, Klopp insists the fixture congestion caused by their progress to another final will make the quadruple harder to achieve.
– ‘Special moment’ –
“The quadruple talk I can’t believe it. Qualifying for this final makes the quadruple even more difficult,” he said.
“I don’t think we have a full free week before the last matchday. But we beat the strongest team in the world and that’s a pretty special moment.”
There is no rest for Liverpool in their trophy chase as they host Manchester United on Tuesday.
“In three days we play against United, who are fighting for a Champions League place. Historically it is not a friendly game,” he said.
“Then we play Everton, with the situation they are in it will not be a friendly game. It (the quadruple) is just incredibly unlikely but let’s go for it.”
Pep Guardiola’s decision to field a weakened team will be second-guessed, but City’s manager is adamant he was right to leave Kevin De Bruyne on the bench after the Belgian needed stitches in a foot injury.
With City’s treble bid over, Guardiola has to revive his fatigued players quickly if they are to hold off Liverpool in the Premier League and beat Real Madrid in the Champions League semi-finals.
“I have a lot of confidence in my players and the selection. We had a terrible time in terms of fixtures and travel. That’s why we need the fresh legs,” he said.
“The first half we were so passive. We were scared to support our team-mates. In the second half we showed incredible pride when you talk about being tired. We had chances for extra-time.
“We tried to put energy in the players, but sometimes it happens. It is Liverpool.”
Guardiola refused to blame Zack Steffen for City’s defeat as the American keeper’s mistake led to Mane scoring Liverpool’s second goal.
“It was an accident. Ederson was close (to doing it) in the other game. The way we use our keepers, the way we move them around, I would say the averages, it can happen,” he said.
“We have four days until the next game (against Brighton). We have to recover well for the two competitions we are in.”