The former Chelsea man scored a thunderous equaliser following Edin Dzeko's opener, but picked up the knock in the opening half, and continued until he was replaced by Joe Allen in second-half stoppage time.
"He got a knock just before half-time on his thigh," Rodgers told reporters.
"He wanted to give it a go in the second half but I think he'll be a doubt for the [England] game on Wednesday.
"It's unfortunate because he was terrific today. His hold-up play, his movement, his pace. He was a real, real threat. His combination with Suarez and Downing and Henderson up front was outstanding."
Sturridge himself confirmed that he struggled after the break due to the knock, although he expects to return to full fitness soon.
"I did it in the first half and throughout the game I couldn't sprint," he explained to Sky Sports.
|RODGERS HAILS SUAREZ & STURRIDGE
|7/1||Liverpool are 7/1 with Bet365 to finish in the Premier League top four this season
"After I did it, I couldn't really open up properly. Hopefully it's not too serious and I'll be okay for next week's game."
Pepe Reina's rash decision to rush from his goal line allowed Sergio Aguero to snatch a point for City after Sturridge and Steven Gerrard had given the Reds a 2-1 lead and Rodgers, despite being disappointed with the result, hailed his side's performance against the champions.
"It was an outstanding performance at a notoriously difficult place for teams to even score a goal," said the Northern Irishman. "I don't think they've conceded here [in 2013].
"What was important for me was to see the confidence of the players, the desire, the quality and the efficiency of their game. I don't think anyone would deny that we probably deserved to win that game.
"The disappointing thing was that it typified our season, really, where we've been outstanding in our game and the model of our work but mistakes have cost us. That's all a part of our growth.
"I was really disappointed for them because they'd put so much into the game. Obviously Aguero's finish is unbelievable but from our perspective we're bitterly disappointed he was even in that position.
"It was a mistake, everyone was clear on that, but I can't fault the players. I thought they were absolutely brilliant today. We showed great character.
"We might be missing two or three players who can really help the group that clubs like Manchester City have, but I don't think you can fault the players for what they're giving in the game.
"Once we cut out those mistakes - which we will do, there's no question about that - draws turn into wins and we can be a real force, because we've got some really talented players. The group is still growing and building."