City are no longer the dreamers they were in the recent past but a hardened club expecting to be challenging for trophies every season.
They remain alive in four competitions this year and Nasri feels winning one of them is the very least of their objectives.
The first of those trophies is on the line as City take on Sunderland in the Capital One Cup final on Sunday.
Midfielder Nasri said: "I think it is just another game.
"You have to be focused when you sign for this team, you know the target is to win a trophy every season.
"We know we have world-class players in the team, everyone at the club has invested a lot to build a big team. The minimum we can do is to win a trophy.
"When we go to Wembley we should not be surprised (and thinking), 'wow, something amazing'. It is just another game. We have to win and do our job."
Nasri has been integral to City's drive for success this season, enjoying a new lease of life under Manuel Pellegrini.
The French playmaker was laboured in Roberto Mancini's final campaign, to the point when the then manager joked he even wanted to "punch" him.
Nasri, a high-profile £24million signing from Arsenal in 2011, attributed his poor form to a loss of confidence stemming from negative reaction to his and France's performances at Euro 2012.
He feels that has now been fully restored since Pellegrini took charge at City and, even though he is still to get back into full flow after a recent knee injury, he is enjoying his football.
The 26-year-old said: "With him the confidence is a major factor.
"Everything has been okay since the first training.
"We talked together and he told me I could be important again for the team.
"After that we just talk all the time together, when everything is okay, when something is wrong.
"And that is what I like about the manager is we can share things and, as well, the way he wants this team to play is what I like.
"I try to give my best for him."
City are firm favourites to overcome a Sunderland side threatened by relegation, although the Wearsiders have been a troublesome opponent for them of late.
Sunderland have won 1-0 on each of City's last four visits to the Stadium of Light - but Nasri insists that counts for nothing.
He said: "I am confident if we play our football and play the way we have been playing since the start of the season we are going to succeed."
City also know from painful experience how odds can be overturned at Wembley, having been stunned by Wigan in one of the great FA Cup final upsets last season.
Nasri said: "Of course that gives us extra motivation but we have to respect every opponent. No one is going to give us a trophy."
Defender Aleksandar Kolarov is confident City will prevail if everyone is on top form.
The Serbian left-back said: "We are full of confidence in the Premier League. My opinion is we have the best team.
"We know every final is a big game and I think it is 50-50, our chances of winning.
"They beat (Manchester) United and have played some good games in the last two months.
"But if we are 100 per cent we are better than them. We have to show that on the pitch.