Since the Bosnia international's ?27million move from Wolfsburg last month he has scored two goals - both against League One side Notts County - in eight appearances.
His strike was the fourth goal in the 5-0 FA Cup fourth round replay win over County on Sunday and came in the 89th minute, although he could have added another in added time when clean through only to shoot straight at goalkeeper Stuart Nelson.
Edin up: Dzeko scored his second goal since his ?27million arrival from Wolfsburg in the 5-0 FA Cup win over Notts County
Dzeko admits he is still trying to adapt to the more physical nature of football in this country but has no doubts he will get to grips with the challenge.
'It's harder here but I will get used to it. It is something new for me,' he said.
'The referees don't whistle for everything here - in the Bundesliga every small contact is a foul.
'The coach (Roberto Mancini) says to me it is different in Italy and Germany as the referees whistle everything.
'I hope I can get used to it, and have to get stronger. I have to play stronger.
'In some situations in Germany where I am not so strong it is no problem but in England it is different. You have to fight for every ball.
'I am OK mentally. When I don't score for two or three games and then lose the ball I always keep my head up.'
City slickers: Dzeko is happy to be playing alongside Argentine striker Carlos Tevez
Dzeko played alongside temperamental young Italian Mario Balotelli against Notts County but rarely did the pair threaten either individually or as a pair.
Tevez, the club's top scorer who registered his 50th City goal in 68 appearances, was on the bench on Sunday but remains the club's top striker.
However, Dzeko is confident he can forge profitable partnerships with both the Argentina international and Balotelli.
'We showed in the second half how we (he and Tevez) can play together and also in the first half I played well with Mario and we understood each other,' said the 24-year-old.
'Everyone could see it. Communication is important and when you have an understanding with someone on the pitch it is the most important thing.
'Carlos has been here a long time and I am the one getting used to everything, so when I settle we will all play much better.
Floored: Dzeko's starting partner against Notts County, Mario Balotelli, had to be taken off after an injury
'I know I can play much better and I will work hard and show people. Strikers are expected to score and I have two goals in eight games.
'When you see this, you can think it's not good, but I try to work also for the team, not just to try to score.
'I try to assist team-mates. I am not a player who stays on the edge of the box and waits for a chance.'
City hope to have Shaun Wright-Phillips, out with a back problem, back for Thursday's Europa League last-32 second leg tie against Aris Salonika.
But Nigel de Jong is expected to miss the next two matches with an ankle injury, while James Milner (hamstring) should be available for the visit of Fulham next Sunday.
However, goalkeeper Shay Given, being kept out of the first team by Joe Hart, will visit a specialist in London this week to discover whether he requires surgery on a shoulder problem.
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Explore more:People: Edin Dzeko, Shay Given, Joe Hart, Shaun Wright-Phillips, James Milner, Roberto Mancini, Mario Balotelli Places: London, Argentina, Bosnia, Germany, Italy, United Kingdom