Rodgers was dismayed with a series of decisions that he felt went against his side in the 2-1 defeat at the Etihad Stadium, labelling the performance of the officials as "horrendous".
Raheem Sterling saw an opening goal ruled out for offside, despite replays suggesting he was onside, while Luis Suarez was denied a penalty in the closing stages as his team looked to salvage a point.
The Northern Irishman also questioned the decision to appoint Bolton-born referee Lee Mason for the encounter stating: "Hopefully we won't have a Greater Manchester referee with Liverpool-Manchester games in future."
The FA took a dim view of the comments and confirmed they have launched an investigation.
Rodgers has subsequently been charged by the governing body and has until January 8 to respond.
A statement by the FA read: "Liverpool manager Brendan Rodgers has been charged by The FA over post-match media comments he made following his side’s game against Manchester City on 26 December 2013.
"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."