The striker on Saturday earned a 1-0 pre-season win over Sunderland at the rain-drenched Hong Kong Stadium to give Manuel Pellegrini his first trophy since taking over at City, albeit in a friendly competition.
It was a second goal in as many games for Dzeko, who has been linked with a transfer, after the Asia Trophy semi-final win over South China and it helped City bounce back from defeats in their earlier South Africa tour by Supersport United and AmaZulu FC.
The Bosnian now wants to replicate that success when the Premier League starts in three weeks' time when City will attempt to wrestle the title back from derby rivals Manchester United.
Dzeko told Sky Sports: "Two games, two wins. It is definitely good after we lost the first two games of pre-season. I think it was very useful for us and also for the coach to see his new players."
He added: "We had a good pre-season with the new manager and all of us are definitely looking forward to the Premier League. We want to achieve some good things next season."
Dzeko was guilty of a dreadful miss from a second-half penalty against Sunderland and unsurprisingly he did not want to dwell on it.
He said: "That is football, that is life. But we won at the end so it is okay."