The Bosnian striker looked out of sorts as City drew 0-0 with Aris Salonika in Greece in the Round of 32 of the Europa League and Mancini said he has to improve.
"I expect more [from Dzeko]," said Mancini. "He needs to improve. He's a good player. We had a great chance with him and he should have scored.
"Dzeko needs to play and it's important that he improves quickly. With Dzeko playing, Shaun should be crossing the ball more.
"But we only had one cross in the second-half and that was from Gareth Barry."