France, eliminated in the group stages of both Euro 2008 and the 2010 World Cup, face England on June 11 in Donetsk before playing co-hosts Ukraine and Sweden.
"The last eight is certainly within our reach. We have the potential to qualify," Nasri told reporters at France's Clairefontaine training facility.
"Obviously, it's better to play England first, when Rooney is still suspended," he added.
"I only realised how crazy it had all been when I watched the game again," Nasri said, referring to the two stoppage-time goals which helped City defeat Queens Park Rangers to win the club's first league title in 44 years.
"I am a bit tired, I did not sleep enough. We did a lot of partying. But I will recover fast here," he added.
"It was a fantastic moment for the club and for me as well.
"I managed to make an impact at the end of the season. I also think I improved mentally and defensively at City."
