Captain Gerrard, who has just returned from a long layoff with a groin injury, clinically converted a 13th-minute penalty to put seven-times winners Liverpool in the driving seat for the second leg at Anfield in a fortnight.
City, who were knocked out of the FA Cup by Manchester United on Sunday, improved after the break following a woeful first half but were still well short of the form that has propelled them to the top of the Premier League.
"The first half we didn't play well because after six months it can happen for the first time," City manager Roberto Mancini told the BBC.
"It is clear that without three or four players it's more difficult but in the end we didn't deserve to lose the game. We played poorly in the first half but the result is not right. The right result was a draw."
Goalkeeper Joe Hart had to make two fine saves in the opening minutes, once from Gerrard and then from a deflected Stewart Downing effort, but he was beaten from the spot when Gerrard drilled his shot low into the corner after Stefan Savic's clumsy tackle on Daniel Agger in the penalty area.
The home side, who beat Liverpool 3-0 in the Premier League last week after a surprise defeat by Sunderland on New Year's Day, enjoyed long spells of possession after the break but rarely opened up a massed Liverpool defence.
"We wanted to come here and get a clean sheet and a goal which we did but we know there is no way this tie is over," Gerrard said. "We will have a very tough match in two weeks' time so the job is half done."
"It's games like this I've missed," England midfielder Gerrard, who has suffered a frustrating 12 months largely on the sidelines, added.
