City took the lead in the 40th minute with a header from Joleon Lescott but were flattered by it and a point was the least the visitors deserved.
Mancini said: "I'm very sorry today for the players because it was difficult after Madrid but I'm worried because we conceded a goal. We need to improve and we need to work.
"In the last four games we've conceded three goals from set-pieces. This can't happen. I'm frustrated but the players are frustrated about this. If you want to win, clean sheets are important."