Rodgers was angry with an offside flag against Raheem Sterling before he went on to score and he felt Luis Suarez was denied a late penalty.
He also questioned the appointment of Bolton referee Lee Mason.
Rodgers said: “Hopefully we won’t have a Greater Manchester referee with Liverpool-Manchester games in future.”
He added: “We had nothing that went our way at all.”
Liverpool were top of the Premier League at the start of Boxing Day, but dropped to fourth after City’s comeback victory at the Etihad Stadium.
Manuel Pellegrini’s side fought back from Philippe Coutinho’s opener to move within a point of leaders Arsenal after goals from Vincent Kompany and Alvaro Negredo.
The defeat for Liverpool leaves them three points adrift of Arsenal, who beat West Ham, with City and Chelsea in second and third respectively.
Rodgers was particularly infuriated by the decision against Sterling, who put the ball in the net after being incorrectly flagged offside when the game was still goalless.
The Northern Irishman also claimed Suarez had his shirt pulled by Manchester City defender Joleon Lescott inside the home penalty area in the late stages.
“I never go on about officials but I thought they were horrendous,” he said.
“The linesman gave Raheem offside in the first half but they were not even on the same cut of grass. If you are working at this level you have got to get those right.
“I’m asking young players to make those runs, he does it perfectly, and is given offside.
“There was another incident in the second half when Luis should have had a free-kick on the edge of the box and arguably there was a penalty late on.
“Luis can’t jump because [Lescott’s] tugging at his shirt.”
Rodgers does not believe that Mason, who is from Bolton, should have been put in charge of the game because of his proximity to Manchester.
“I was surprised that we are playing in Manchester and we had a referee from Greater Manchester,” he added. “I was surprised when I saw it but that’s by the by.
“For Liverpool against Manchester City, I don’t think we’d get an official from Wirral.”
City boss Pellegrini said he was happy with his team’s response to Coutinho’s opener and their handling of in-form Suarez.
The Uruguay strker, who again captained Liverpool in the absence of injured skipper Steven Gerrard, had scored 10 goals in his previous four games heading into the Boxing Day match.
“It is not easy when you face such a difficult team, especially on the counter-attack when you are losing 1-0,” Pellegrini said.
“I think today we defended very well especially against Suarez.”
Written by Steve Milne – Have your say below 🙂
