Before the draw, Liverpool had been due to face Everton on April 8, but the match has now been switched to a 12.30pm kickoff on April 7, with the match being held less than three full days after the first leg of the European clash with City.
Liverpool will benefit from more recovery time ahead of the second leg at the Etihad Stadium on April 10, but Klopp feels that the encounter with Everton should be staged at "a normal time."
At a press conference, the 50-year-old told reporters: "I'm already angry as the Everton game has been moved to 12.30pm on Saturday. Now it's Wednesday night and Everton on Saturday morning.
"Whoever made the schedule and had us playing on the Sunday thought Liverpool weren't going through. Then oops, Liverpool are through. City play at half five on the Saturday - those five hours are a big difference. Put the Everton game on a normal time - not at breakfast."
Liverpool will be bidding to reach the semi-finals of the Champions League for the first time since 2008, while also attempting to finish in second place in the Premier League for the first time since 2014.