Rodgers was unhappy about several decisions made by the officials during the Etihad Stadium encounter, which the hosts won 2-1 after trailing 1-0.
And, in his post-match remarks, he questioned the decision to place a referee from Greater Manchester in charge of the contest.
He has now been handed an FA charge and has until 6pm on Wednesday to respond.
An FA statement read: "Liverpool manager Brendan Rodgers has been charged over post-match media comments he made following his side's game against Manchester City on 26 December.
"It is alleged the comments by Rodgers called into question the integrity of the match referee, and/or implied that the match referee was motivated by bias; and/or brought the game into disrepute; and/or amounted to a failure to act in the best interests of the game."
Rodgers was unhappy about the incorrect decision to rule Raheem Sterling offside when he was through on goal in the first-half and also felt Liverpool could have had a pair of penalties after the break.
Speaking after the game, he said of the officials: "I thought they were horrendous in terms of performance.
"Hopefully we don't have another Greater Manchester referee again on a Liverpool-Manchester game.
"I was surprised we are playing in Manchester and have a referee from Greater Manchester. I am sure we won't get someone from the Wirral for Liverpool-Man City."
Rodgers then stood by his comments the following day and denied he was trying to attack Mason.
"I certainly wasn't questioning the integrity of referees," he said.
"(The comment) was more than logical in terms of having a referee from that part of the world refereeing a game in Manchester.
"I wouldn't suspect that Mike Dean, from the Wirral, has refereed many games for Liverpool over the years.
"I was only speaking honestly after the game. I think the FA and the Referees' Association know perfectly well I am someone who engages in supporting the referees."
StenchTrench & Clogs... Chippy Chippy Chippy. Boris Johnson was right. You do yourselves no favours. He implied the ref was biased. Not fat, not incompetent, not stupid. He more or less called the ref a cheat. A three game touch line ban.- popularpete