The Italian refused to expand on what he thinks is currently going wrong for his team.
Mancini, whose team host Sunderland on Saturday before the international break, is sure he can find a solution to his team's issues and has promised he will rectify their issues quickly.
He said: "I know the problem and I will resolve it very quickly. It's my problem and my job and I will solve this problem.
"If we want to play in the Champions League we have to play better.
"We have to run and fight. It's not enough to just pass. Champions League is another situation - different from the championship.
"We have to run and fight. It's not enough to just have quality. If you don't run like Dortmund did, then you have a problem.
"Our performance was very poor but I think that in the end of the group this point could be very important."
Mancini's plans for the Sunderland game have also been hit by Javi Garcia limping out of the Dortmund game with a hamstring problem.
City failed to progress to the knock-out phase last season after collecting just a point from their opening two group matches.
They now face a double header with Ajax before a home game against Real Madrid and a trip to Dortmund.
England goalkeeper Joe Hart, 25, who was outstanding against Jurgen Klopp's side admits his team's prospects of qualifying would have been slim without Balotelli's late penalty at the Etihad Stadium.
He said: "I hope it's important and not a wasted effort.
"I hope the effort we've made in both of those games isn't wasted and we can focus on qualifying but it shows what a group we're in.
"It would have been nice to win the game but we've come out alive and the group's still alive for us."
-AAP
