The Liverpool boss was annoyed that Raheem Sterling had wrongly been given offside in a goalscoring opportunity and Luis Suarez hadn't been awarded a penalty in the 2-1 defeat.
"Hopefully we won't have a Greater Manchester referee with Liverpool-Manchester games in future," he said after the game.
"I was surprised that we are playing in Manchester and we had a referee from Greater Manchester.
"For Liverpool against Manchester City, I don't think we'd get an official from Wirral."
He later explained his comments, saying: ""I certainly wasn't questioning the integrity of referees," he said. "It was more than logical (to question) having a referee from that part of the world ref a game in Manchester."
He has until 2nd January to reply to the FA.