Blanc stated after Les Bleus' 1-1 friendly draw with Chile in Montpellier earlier this month that the former Marseille man "has the ability to do better", and that the uncertainty over his future was affecting his game.
The 24-year-old was involved in three of City's goals in their 5-1 Premier League win at White Hart Lane after finalising his protracted move from Arsenal last week, but has vowed to keep on improving if Blanc is not yet satisfied.
He told France Football: "This could maybe mean that he rates me highly. But, after all, it's not by repeating it publicly that it's going to get better. It happens that you can have off days.
"I have a good relationship with Laurent Blanc and especially [assistant coach] Jean-Louis Gasset.
"I know they have faith in me. But I would prefer that the coach tells me certain things face to face.
"Now, if that's really what he thinks at the moment, it is up to me to do more and show him he is wrong."
Nasri is already feeling at home at the Etihad Stadium after joining on a four-year contract in a deal worth a reported £24million.
"My integration is fast and ideal," he added.
"From the beginning there was unanimity on my arrival.
"From the coach Roberto Mancini, the chief executive Garry Cook, to the chairman Khaldoun Al Mubarak, I felt that everyone wanted me.
"The other players teased me at my first training session. They said to me, 'You took your time to arrive - we have been waiting more than one and a half months for you!"'
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
Jamaica is in need of a win against the U.S. Get the jersey of the Reggae Boyz.
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
Germany is one of the top teams ever and they will play the US on Sunday.