The Reds fell a goal behind when Edin Dzeko scored in the 23rd minute before Daniel Sturridge and Steven Gerrard edged the visitors ahead but a late Sergio Aguero goal ensured both teams took a point each.
Rodgers, who saw his Reds remain seventh on the table, felt it was a fairly positive result for the Merseysiders.
"That was an outstanding performance today coming here, which is notoriously difficult place where it is even difficult to score goals," Rodgers told Sky Sports.
"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."