The Football Association (FA) punished Klopp for questioning the integrity of match official Kevin Friend in reference to decisions made in the Premier League encounter at the London Stadium.
The Reds boss suggested Friend favoured the home side in the second half of the draw, which came as a setback to his side's title challenge.
Liverpool went ahead through a Sadio Mane goal, but the officials failed to spot James Milner in a clear offside position in the build-up, something which Klopp suggested influenced Friend's decision making in the rest of the game.
"There were so many situations where it was 50-50 or 60-40... [he gave a] free-kick for the other team," the German told Sky Sports after full-time.
"As a human being, I know if I make a big mistake in the first half, I don't want to open the gap even more."
The FA released a statement on Thursday announcing the sanction.
It read: "Jurgen Klopp has been fined £45,000 after accepting an FA charge for comments made following Liverpool’s league game against West Ham United on 4 February 2019.
"His comments made during a post-match interview breached FA Rule E3(1), as they questioned the integrity of the match referee and/or implied bias."