Nasri supplied the crosses for Dzeko to score his first two goals and he also played his part in the run up to Sergio Aguero's strike
"I think the last time I scored four was for Wolfsburg in Germany," the Bosnia international said on ESPN.
"Today was something special for me, to score four goals in the Premier League is fantastic.
"I think we're getting better and better. I hope we can improve in the next game and try to win every game."
Nasri added: "This is a tough place to win. I had a good game but the most important thing is we won 5-1 and sent out a signal to other clubs.
"This is just start of the season, it's important to keep our confidence, but I'm convinced we have a great team here and can win things."