Stevan Jovetic opened the scoring four minutes before half-time on Monday night as he slammed the ball beyond Simon Mignolet from inside the area, after Nasri’s cross had caught Liverpool debutant Alberto Moreno flat-footed.
Jovetic then rounded off a fine flowing move to double City's lead on 55 minutes before Sergio Aguero stepped off the bench to put the game beyond Liverpool’s reach with just his second touch.
A late Pablo Zabaleta own-goal helped restore some pride for the visitors, but Nasri says it was vital to claim a convincing early victory over one of their title rivals.
He told Sky Sports: "I think every game that we play at home against a team of the big four for us is like six points."
City also have home games against Chelsea, Tottenham and Manchester United in the first three months of the season, and they also travel to another title contender - Arsenal - on September 13.
"We have to make a statement in those kind of games," he added.
Speaking of team-mate Jovetic, who was named Sky Sports' man of the match, Nasri added: "Last year, unfortunately, he was injured a couple of times.
"We saw in pre-season that he was on fire and today he scored two important goals and I think it’s just the start of a big season for him."
Jovetic endured a frustrating first season at City as injury problems saw him restricted to just 11 Premier League appearances following his reported £22million summer switch from Fiorentina.
After an impressive pre-season, the 24-year-old has worked his way into Manuel Pellegrini's starting line-up for the opening two games of this campaign and is hoping to remain there.
Jovetic said: "There wasn’t so many beautiful moments up until now because I had so many problems last year, but I don’t want to think about that, that’s the past.
"Now I just want enjoy things with this team and these players to win more titles.
"It’s difficult (to stay in the team), I know that. But I’m not thinking when I go out onto the pitch. My job is just to do my best."
Asked if it felt sweet to beat last season's closest title challengers, Jovetic replied: "Yes, I think so because Liverpool is one of the teams going for winning the Premier League and we knew that.
"Today we played very well. In the end we won 3-1 and it was an important victory for us."
"...there is no excuse for coming on here and deliberately talking complete and utter nonsense."....exactly! About time you realised that Jimi.- bernsteinforpm