Klopp's side face a Saturday lunchtime kick-off against Everton next month and the Reds boss is unhappy with the lack of recovery time after the quarter-final first leg against City.
Liverpool have only 63 hours between the final whistle of the City showdown at Anfield on April 4 and kick off in the derby at Goodison Park on April 8.
The second leg against City in Manchester is on April 10.
City face Manchester United on the same day as the Merseyside derby, but play five hours later than Liverpool.
"There will be a point when I am looking forward to that game but at the moment I am already angry because I heard a second ago the Premier League will put our game against Everton at 12.30 on the Saturday," Klopp said.
"I know countries where they cancel whole match days, so teams can be in the best shape.
"We play Wednesday night against Manchester City and then play Everton at 12.30 three days later.
"That means the players get up on Thursday and have lunch or breakfast and then we train and next day we are second-day recovery and then you start at 12.30 (on Saturday).
"Can you imagine how big the difference is in these five hours? It means the world in preparation and recovery.
"We take it like it is but if I cannot be angry about something like that any more and have to be politically correct and say nothing then I am dead because that doesn't work.
"Obviously whoever made the schedule didn't think we'd go to the quarter-finals because (the derby) was a Sunday game. Oops, it is only Liverpool."
When Klopp was asked whether he wanted the Everton match moved, he almost lost his temper and had to stop himself swearing.
"No, I'd like it at nine o'clock in the morning. What the f...?" he said.
"At three o'clock normal game. Put it on at a normal time and not at breakfast."