The £27million Bosnian ended an 11-game goal drought with the winner in the Premier League leaders' 1-0 win at Wigan on Monday night.
Dzeko began the season in blistering form, with 13 goals in 14 appearances, but his recent barren spell had attracted criticism and fuelled speculation over his future.
But the 25-year-old told City TV: "It was just a matter of time.
"It is always like this. Sometimes you score a lot of goals, sometimes you can't score even from a 100% chance.
"But that is football. I am happy for me and happy for the team that I scored again and we won the game."
Dzeko's 22nd-minute header at the DW Stadium lifted City back into a three-point lead at the top of the table.
Goalkeeper Joe Hart was also pleased to see the former Wolfsburg forward back on the scoresheet, even though he had not been worried about his form.
Hart said: "We're not interested in what is said outside the club.
"We are very much a team unit and we are very much rooting for Edin to do well.
"We are over the moon for him. That is the kind of thing he does and it is no fluke he scored those goals at the start of the season."
