Daniel Sturridge cancelled out Edin Dzeko's early opener, with City boss Roberto Mancini feeling Reds defender Daniel Agger should have been punished for a foul on the Bosnian.
Referee Anthony Taylor played on and despite the boos, Liverpool opted against putting the ball out of play with the City striker laid on the turf as Sturridge slotted in.
After Sunday's Premier League clash at the Etihad ended 2-2, Rodgers said: "The first goal was clear. Both bodies get tangled up, Dzeko thinks it's a free-kick but you're talking about a minute or so after (until Liverpool scored).
"The referee told a couple of players - Daniel Sturridge and Steven Gerrard - to play on which is why they kept going.
"There was one in the second half when Daniel kicked the ball out. There was no injury to Dzeko, it was purely the referee's decision.
"The controversy probably takes it away from what was a great strike from Daniel."
Despite failing to secure the spoils having taken the lead from Steven Gerrard's superb 30-yard dipping volley, Rodgers was pleased with the performance.
He was unhappy with the mistake by Jose Reina that led to City's equaliser, the goalkeeper charging out to the edge of his penalty area only to see Sergio Aguero turn and rifle in from a tight angle.
"That was an outstanding performance coming here, which is notoriously difficult place where it is even difficult to score goals," Rodgers added.
"We were brilliant. The only disappointment is that we were outstanding in our work but mistakes have cost us. Aguero's finish for the second was unbelievable but from our perspective we are bitterly disappointed he was in that situation.
"It was a mistake, everyone is clear on that, but I can't fault the players."
There was yet more praise for Gerrard, with Rodgers saying: "It was a brilliant goal from him to beat Joe Hart from that distance. I thought his performance was immense."