In three years since its opening, at the Emirates Golf Club the entertainment complex has broken records and is ranked only second to Topgolf Las Vegas
The German manager said referee Kevin Friend's performance was affected by the decision to allow Sadio Mane's opening goal, which should have been ruled out for offside.
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.
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Six WSL games played at the Emirates this season were watched by an average crowd of just over 52,000