Dzeko joined City in a £27million deal from Wolfsburg in the January transfer window, but has so far had a slow start at Eastlands.
“I expect more for Dzeko – he needs to improve,” said Mancini. “He is a good player.
“I think he has the same difficulty as (Fernando) Torres at Chelsea because when you arrive in January you don’t know your team-mates, it is not easy.
“He can change in every game. It is important that he improves very quickly. We should cross the ball more to him.”