With Liverpool having come from behind to lead 2-1 with 12 minutes to go the Spain international rushed from his goal in an attempt to beat Sergio Aguero to the ball.
The Argentina international was too clever for him, however, and having turned Reina on the left edge of the penalty area he drilled in the equaliser from a narrow angle.
“It was an outstanding performance coming here, a notoriously difficult place where it is even difficult to score goals,” said Rodgers.
“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 inspirational captain Gerrard, whose superb dipping 30-yard volley put Liverpool ahead after Daniel Sturridge had cancelled out Edin Dzeko’s opener to ensure they went into the interval on level terms.
“It was a brilliant goal from him (Gerrard) to beat Joe Hart, who is 6ft 5 ins, from that distance,” added Rodgers.
“I thought his performance was immense.”
Sturridge’s goal, his fourth in six games since his £12 million move from Chelsea last month, was another clinical effort from the edge of the area against his former club.
The goal was surrounded by controversy though as Dzeko was laid out on the turf in Liverpool’s half after a tackle from Daniel Agger while Liverpool played upfield to score.
“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 (before Liverpool scored),” added Rodgers.
“The referee (Anthony Taylor) told a couple of players – Daniel Sturridge and Steven Gerrard – to play on which is why they kept going.
“There was no injury to Dzeko, it was purely the referee’s decision.
“That (the controversy) probably takes it away from what was a great strike from Daniel.”
Sturridge is a doubt for England’s midweek friendly against Brazil with a thigh injury.
“He got a knock just before half-time on his thigh and he wanted to give it a go in the second half,” said the Liverpool manager.
“I think he will be a doubt for the game on Wednesday, which is unfortunate because he was terrific.
“His hold-up play, movement and pace was a real threat and combination with Luis Suarez, Stewart Downing and Jordan Henderson up front was outstanding.
“He will have a chat with our doctors and he will speak with the England set-up.
“They might want to have a look at it but at the moment he is obviously struggling.”
