The Bosnian struggled for regular starts under Roberto Mancini, but appears to have been given a fresh lease of life by new City boss Pellegrini.
Though Dzeko did not score in the convincing victory over the Magpies, he was pleased with the performance and happy to be involved.
"I think we played a fantastic match, not only for 45 minutes, but for 90 minutes, which is what the manager expects from us," Dzeko told Sky Sports.
"We played the first game at home and we wanted to show everyone what we are capable of. We scored four goals and we could maybe have scored a few more.
"I wanted so badly to score, but at the end, we won the game, we have three points and we scored four goals. The next games are coming and I'm ready.
"The new manager brings something different to us, especially to me. He gave me confidence and that's what I needed."
Yaya Toure scored City's third with a curling free-kick and the Ivory Coast midfielder was buoyed by the 2011/12 champions' start to the new season.
Toure said: "It was a fantastic result and a fantastic beginning.
"We know the Premier League is very, very tough, but we played very well and full credit to all the team. We worked really hard to try to kill the game in the first half.
"The target of the club this year is to do fantastic things in the Premier League and Champions League, and I hope this year is going to be the time for us."