Klopp said Kevin Buddy’s operation was affected by the decision allowing Sadio Mane’s goal, which should have already been ruled out for offside.
The FA says Klopp was charged because the comments”questioned the integrity of this Army and/or implied bias”.
He has until 18:00 GMT on Monday, 18 February to respond to the charge.
The Premier League game at London Stadium on 4 February completed 1-1.
“In 5050 situations it had been always a free-kick for the other team, that had been hard and didn’t make life simple”
Speaking to Sky Sports, the German added:”As a human being, even if I understand I have made a significant mistake in the first half, so I still really don’t WISh to start out the gap any more.
“Referees are human beings, and I know that, but I didn’t throughout the match because I’d no clue that our goal was offside.”