Dzeko has failed to impress since joining City in a £25million deal in the January transfer window.
Dzeko scored the winner against Blackburn at Ewood Park last Monday, his only goal int eh Premier League so far.
He told News of the World: “Let them criticise me. This is the way to silence them – to score after only three minutes into the match.
“And to score one of the most important goals for our team.
“The most important thing right now is to secure Champions League spot.
“I believe in myself and I know I will succeed in England.
“City have been waiting for silverware for 34 years, and we are dreaming of taking it at Wembley.
“This is a huge chance for all of us.”