The Northern Irishman questioned the decision to have referee Lee Mason, from Greater Manchester, take charge of the 2-1 defeat to City at the Etihad Stadium on Boxing Day
First-half goals from Vincent Kompany and Alvaro Negredo ended Liverpool's four-match winning run after Philippe Coutinho had put the visitors in front at the Etihad Stadium.
The Merseyside outfit had their chances to secure at least a point in the second half, with Raheem Sterling wasting the best of them when he blazed over the crossbar from close range.
The lively Sterling had been incorrectly flagged offside when he raced clear in the first half and Bolton-born referee Lee Mason turned down penalty appeals when Luis Suarez had his shirt pulled by Joleon Lescott late on.
Rodgers said: "I was very proud of the players, I thought they were absolutely outstanding, but they had no help whatsoever from the officials.
"I never go on about officials, but today I thought they were horrendous in terms of performance. Nothing went our way at all."
When asked which decision he was particularly irked by, the former Swansea City boss said: "Where do you want me to start?
"I thought the linesman on the offside, he wasn't even on the same cut of grass and if you're working on this level you have to get it right.
"It's not even a difficult one and these are the things we work on and talk about. We're asking the lad to get across and break their line, it's a perfectly timed run and he's given offside when he's through one-on-one.
"They're big moments in big games. There's another incident in the second half where Luis doesn't get a free-kick on the edge of the box where Joleon Lescott comes right through him and was waved play on.
"Arguably it's a penalty at the end because Luis Suarez can't jump where he's got a hold of his shirt. But I thought it was throughout the evening as well. Hopefully we don't have a Great Manchester official again with a Liverpool-Manchester game.
"I was surprised that we're playing in Manchester and they have a referee from Greater Manchester. I'm sure we won't get someone Liverpool v Man City from the Wirral."