Right-back Boateng and his back-four colleagues have helped Joe Hart keep three consecutive clean sheets for the Blues, but two home draws this week have seen City slip further behind leaders Chelsea.
The German World Cup international, a summer signing from Hamburg, admitted: “Of course we’re all disappointed, we want to win these games. It was a difficult game and we wanted to score a quick goal.
“We work as a team, so we must attack together and defend together. Defence at the moment is good, but attacking is not so good. We must score more goals, but that’s not just about the strikers and midfielders.
“We wanted to win as much as the fans did. We want to be higher in the table but with the Birmingham game it wasn’t possible. We have lost two points and we need to get them back quickly.”
Boateng and left-back Aleks Kolarov both enjoy posing a threat on the flanks: “We run a lot, support our team-mates and get crosses in. But teams come with eight or nine men at the back and we must find a solution.”
Meanwhile, City coach David Platt has revealed that taking off top scorer Carlos Tevez before the end was the sensible option despite the crowd’s reaction to manager Roberto Mancini’s decision.
He said: “Carlos has been carrying an injury for a substantial period of time. The last 10 to 15 minutes of any game - and when you expend so much energy in midweek like he did - become very dangerous.
“The one thing we didn’t want to happen was that Carlos finishes up pulling a muscle and is out for three or four weeks, because he’s very important to us.”
Platt shared the dismay at dropping points, adding: “The biggest disappointment is that we were virtually camped out in their half in the second half and had more chances than you would normally have in any match.
“Unfortunately we couldn’t unblock the game - give credit to Birmingham for the way they defended. But the season lasts 38 games. You keep putting points on the board and striving for victories to keep you up there.”