Dzeko scored the only goal in the final of the pre-season tournament on Saturday, as his 20-yard effort saw City beat Sunderland 1-0 in Hong Kong.
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The Bosnian also blasted a penalty well over the bar, in a match that was overshadowed by the injury suffered by City defender Matija Nastasic.
Nastasic fell awkwardly on the poor surface at the Hong Kong Stadium and was carried off on a stretcher, but instead of that, Dzeko preferred to focus on the positives of the club's Asian trip.
"Two games, two wins. It is definitely good after we lost the first two games in the pre-season," Dzeko told Sky Sports.
"I think it was very useful for us and also for the coach to see his new players. Maybe it could be better if the pitch was a little bit better.
"But it was like that because of the rain. But still we won and we are happy.
"We had a good pre-season with the new manager [Manuel Pellegrini] and all of us are looking forward to the Premier League, definitely. We want to achieve some good things this season."
Dzeko, who scored 14 Premier League goals in 32 appearances last term, is competing with Sergio Aguero and new arrivals Stevan Jovetic and Alvaro Negredo for a place up front in the upcoming campaign.