The FA said Klopp had been charged as the comments "questioned the integrity of the referee and/or implied bias".
West Ham equalised through Michail Antonio's goal before the interval but Klopp said Friend "did not want to open the gap any more" in the second half.
"As a human being, if I know I have made a big mistake in the first half, I don't want to open the gap any more," Klopp said after the match at the London Stadium.
"Referees are obviously human beings, and I understand that, but I didn't during the game because I had no clue that our goal was offside."
Klopp has until 1800 GMT on Monday to respond to the charge.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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