The Liverpool manager was charged in the wake of his side's 2-1 defeat at the Etihad Stadium on Boxing Day.
Rodgers called the performance of the officials "horrendous" and questioned the wisdom of allowing Bolton-based referee Lee Mason to take charge of a game involving a Manchester club.
He later denied disputing the integrity of the officials, arguing he was "only speaking honestly after the game".
But Liverpool will not contest the FA's charge, and Rodgers is now likely to be fined once the case is heard.
The Irishman was infuriated by an incorrect offside decision against Raheem Sterling with the City game still goalless, and he also felt Luis Suarez should have been awarded a second-half penalty.
Explaining his post-match comments the day after the defeat Rodgers said: "I certainly wasn't questioning the integrity of referees.
"(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."
Rodgers is always supporting Referees? Do me a favour. More like he is looking for an excuse to blame the officials rather than face up to the fact his team just lost. People should realise that wrong decisions are part of football always has been and always will be thats untill they replace the Ref and lino's with cameras. And when that day comes Football will die. Refereeing (linesman) is not an easy job in the best of times and without them we have no football. Obvisiously poor performing Refs should be demoted and they are, and Refs like Clattenburg should be investigated, but that said Managers should not be allowed to personally abuse any of the officials on camera it doesn't do anyone any favours.- dhekelian