Big-spending City remain a disjointed side and draws against Aston Villa, Wigan Athletic, Fulham and struggling Birmingham, who missed a penalty and were the more dangerous side throughout, showed how much work manager Mark Hughes still has to do.
City's point moved them up to fourth place on 19, eight behind leaders Chelsea, who hammered Bolton Wanderers 4-0 on Saturday.
Champions Manchester United are second on 25 after beating Blackburn Rovers 2-0, with Arsenal third on 22 following their 3-0 victory over Tottenham Hotspur who are fifth on 19.
Liverpool, who had two players sent off in a 3-1 defeat at Fulham, and Villa, who drew 1-1 at Everton, both have 18. Birmingham climbed to 14th on 11 points.
LOWEST SCORERS
Birmingham, the lowest scorers in the Premier League with just eight goals from their first 10 games, had the best of the first half with Shay Given forced to make several good saves as Christian Benitez looked particularly dangerous.
They should have taken the lead 10 minutes after halftime when Nigel de Jong handled in the box but Given came to the rescue again when he saved James McFadden's penalty.
City were without Emmanuel Adebayor with an ankle injury and the starting strike duo of Roque Santa Cruz and Carlos Tevez struggled to make any impact.
Craig Bellamy tried manfully to get things moving and City had plenty of possession and half-chances but Birmingham goalkeeper Maik Taylor was barely tested.
Birmingham had Barry Ferguson sent off in stoppage time to become the ninth red card victim from the weekend's 10 league games.
