The champions dealt an early blow to last season's runners-up with two goals from Stevan Jovetic and a third from substitute Sergio Aguero.
Nasri, who created the second goal for Jovetic, feels that beating one of their rivals for the league crown at such an early stage of the season carries huge significance.
"Every game at home against a team in the big four is like six points," the former France international told Sky Sports. "We had to make a statement; it was important."
Jovetic, who only scored three league goals in an injury-hit campaign last year, was influential for Manuel Pellegrini's side and was rewarded with two neat finishes.
The Montenegro international was delighted to have opened his account for the season in the "important victory" and hopes that it will be enough to keep him in the first team.
"There weren't so many beautiful moments [for me at City] until now," Jovetic remarked, "but that's past. I want to enjoy this season and win titles.
"It is difficult [to stay in the side] but I will just do my best, then [Pellegrini] decides."