The Spain international raced out of his goal to close down Sergio Aguero but failed to divert danger, with the Argentine equalising from an acute angle in the 78th minute.
Edin Dzeko had put the Citizens ahead with a close-range finish after Liverpool had made a bright start to the clash at Eastlands.
It was no surprise to see the Reds finally convert their dominance into goals as Daniel Sturridge scored against his former club and Steven Gerrard netted a long-range effort before Reina’s mistake gifted City a leveller.
“It should have been a win for ourselves, I thought we played terrific and were the dominant team. We scored two wonderful goals and I am disappointed with the goals we conceded,” Rodgers told BBC Sport.
“The first was direct from a throw-in, and the second typifies the growth we need to make to be up there challenging. The template of our game is improving, we need to cut out the mistakes and we can challenge at top of the league.
“Daniel Sturridge has been immense and has given us a tonic, a reference at the front for the team. He is now part of the jigsaw of our growth – we are growing all the time and that is what this season is about.
“We have come to the home of the champions and dominated. We know we can be better.”
Rodgers added that Reds striker Sturridge is a doubt for England’s friendly against Brazil on Wednesday after picking up a thigh injury in the 2-2 draw.
“Daniel has a dead thigh and we will liaise with England. I think he will struggle to make the friendly against Brazil,” said Rodgers.
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