The Bosnia international was used only sparingly by former boss Roberto Mancini last season, mainly reduced to a role off the bench, although he was the club's top scorer in the league.
Dzeko looked in fine form in City's resounding 4-0 win over Newcastle, even if he did not get on the scoresheet himself, and has credited Pellegrini with showing faith in his abilities.
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“I think we played a fantastic match, what the manager expects from us. We played the first game at home and we wanted to show the fans what we’re capable of.
“We could have scored a few more but we are happy with the score. I wanted so badly to score but we won three points and the next games are coming and I’m ready.”
Yaya Toure struck a stunning free kick just after the restart to send the home side 3-0 up, and, after City spent big in the summer to secure four high-profile new recruits, believes the club can challenge for multiple honours.
“We played very well. Full credit to all the team, we worked very hard,” the Ivory Coast international said.
“[We have brought in] amazing, quality players, I think this kind of player will help the squad.
“The aim of the club this year is to do fantastic things in the Premier League and the Champions League, and I hope this year is going to be a good year for us.”