Manuel Pellegrini's side cruised into the fourth round of the FA Cup with an emphatic victory in the third-round replay against the Championship outfit, who had held City to a 1-1 draw at Ewood Park earlier this month.
But Blackburn could not replicate that display as City made it 99 goals in all competitions this season thanks to braces from Alvaro Negredo and Dzeko, as well as a strike from Sergio Aguero in his first game back from a calf injury sustained in December.
City, who sit second in the Premier League and are 6-0 ahead after the first leg of the League Cup semi-final with West Ham, are in the running for four trophies, although the Etihad Stadium club do face a stern test in the last 16 of the UEFA Champions League with a tie against Barcelona.
Dzeko, however, insists that City are keeping their feet on the ground, despite the excellent form displayed by Pellegrini's men in the Chilean's first season in charge.
"I don't think it was easy (against Blackburn) especially in the first half," Dzeko told ITV.
"(The goal scored at the end of the first half) it was very important for us, and also the first goal in the second. As usual we scored some more.
"We are still there for four trophies, but our target is to win every next game."
Dzeko has now scored 15 goals this season and has been a regular in the absence of Argentina striker Aguero, whose return does not worry the former Wolfsburg man.
"Lately I'm playing a lot of games, I feel good and the team is winning," he added.
"It's great news for the team because he (Aguero) is one of the important players for the team."
