David Silva and Sergio Aguero scored before half-time prior to Yaya Toure and Samir Nasri doubling the advantage by the final whistle and the overall performance at the Etihad Stadium was warmly welcomed by Dzeko who was given a start by new manager Manuel Pellegrini.
"I think we played a fantastic match and not only 45 minutes but 90 is what the manager expects from us," he 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 have scored more but we are happy with these four.
"I wanted so badly to score but at the end, we won the game, we have three points and we have scored four.
"The new manager brings something different to us, especially to me. He gave me confidence and that's what I needed."