Dzeko relieved to get off mark
The Bosnian fired home the only goal of the game in the 75th minute, just three minutes after emerging from the substitutes' bench.
And he told Sky Sports 1: "I'm very happy that this goal helped my team to win the game. Sometimes it's difficult, I'm not the first who didn't make the best start but I'm happy because I scored today and helped the team.''
Dzeko's drought has been focused on parallel with that of Chelsea's £50 million man Fernando Torres, who opened his Blues account against West Ham on Saturday.
And Dzeko said: "It's football, Torres scored a lot of goals at Liverpool and changed club, I'm happy for him too because I know what the pressure is. Now we have to look at the future - today was very good, it is a new beginning for me and for City.''
Manager Roberto Mancini added: "I'm very happy for Edin because he deserves to score, he is a good player and a good man. In the first half we played a fantastic game, we should have scored two goals minimum. In the second half the game changed, Blackburn played very strong and hard.''
Blackburn boss Steve Kean said: "We're bitterly disappointed, we gave it a right go. After the first 15 minutes we got to grips in midfield and were in the ascendancy before half-time. Even in the second half we were excellent.''
"There was contact, Jason was saying he wanted to go through and finish,'' he said. "We also thought we had a late shout with Niko Kalinic. On the goal, (Mario) Balotelli was right in front of Paul Robinson so I'm saying that was offside.''
Nevertheless, Kean remains confident of top-flight survival and said: "We feel as a group if we play like that against Bolton on Saturday we can get a win, never mind a draw.
"We're gutted we didn't get anything tonight but if we play like that, we've got a great chance.''