Javi Garcia marked his City debut by equalising with a free header after 35 minutes and the Spain midfielder went close to snatching a last-minute winner.
Garcia was again unmarked, this time at a corner, as he powered a header towards the bottom corner but Asmir Begovic did brilliantly to tip his effort onto the post.
Mancini said: "Here it is always difficult, not only for us but all the teams.
"We had two incredible chances at the end of the game and we were unlucky. It is a difficult pitch for us.
"I think that Garcia scored an important goal and he had another chance.
"He played well. Like Maicon, it was the first game for them and I think both players did a good performance.
"They don't know their team-mates yet and for a first game they did well."