The Reds led at the Etihad through a Philippe Coutinho opener but by half-time, Vincent Kompany and Alvaro Negredo had struck to put Manuel Pellegrini's hosts on course for a 2-1 Premier League victory.
Liverpool were aggrieved early on when Raheem Sterling sprang the offside trap with yards to spare only to be flagged, and Rodgers was also irked by Joleon Lescott's late shirt-tug on Luis Suarez going unpunished.
In the wake of a defeat that left Liverpool fourth, Rodgers questioned the wisdom of assigning Bolton official Lee Mason to the fixture and called the officiating performance 'horrendous.'
But, when asked whether a pending FA charge was of concern, Rodgers said: "I was only speaking openly and honestly, after the game. I think the FA and the referees' association know that I'm someone that engages in supporting the referees.
"I'm not one that is berating referees after games, I'm always respectful and I ask my staff to be respectful, on the pitch we're never chasing fourth officials or anything on a match day. I've had a number of referees in here to help and support what they do.
"I think they know that when I come out and make a statement like I did yesterday, it was obviously emotional after the game of course, but it was something that I will speak honestly on. As I said, whatever action they will take, they will decide.
"I have to speak on behalf of the supporters of the club, a club that has an emotional investment for many, many millions of people throughout the world. As the manager I represent them, and I'm sure where they were throughout the world yesterday they would have been asking the questions on the decision-making, which I repeat I didn't think was so good, after the game.
"In terms of geography, it wasn't the case at all, I certainly wasn't questioning the integrity of the referees. As I said before, I fully understand the job, it was more the logic of it, in terms of having a referee from that particular 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."
The FA's rule E3 (1) outlaws "comments about match officials which imply bias, attack the officials' integrity or which are personally offensive in nature."