The 27-year-old playmaker won the Premier League last season with City but was left out of the France squad for this year's World Cup in Brazil, where the side reached the quarter-finals.
Deschamps later filed a legal complaint for 'public insult' against Nasri's girlfriend, Anara Atanes, for messages she posted on Twitter after the player was omitted from the France squad.
"Let's face it, as long as he (Deschamps) is going to be the manager I don't think I have a shot after everything that has happened," Nasri told reporters before Sunday's Community Shield against his former club Arsenal.
"I will only be 29 in 2016 for the European Championships (hosted by France) but the French national team doesn't make me happy. Every time I go there, there is just more trouble.
"I face accusations about me and my family suffers from it and I don't want to make them suffer, so it's better to stop it and focus on my club career."
Nasri, who has been capped 41 times, has a reputation as a troublemaker and was banned for three matches after launching a foul-mouthed tirade at a reporter following France's quarter-final defeat by Spain at Euro 2012.
The player also missed the 2010 World Cup when former coach Raymond Domenech left him out of the squad.
Nasri said Deschamps was not the only factor that drove him towards taking a decision to quit playing for France.
"He did what he thought was best for his team. I understand his choice, it is not something about him, I don't have any problem with him. It's just everything," Nasri added.
"It is not him who talks in the press, it is the press who say things about me and the players as well.
"Before this World Cup, they were saying that some players complain (about him). Why do you want me to be in the group with some players who can't even be true in front of me and tell me that they have a problem?
"I don't want to be there. I am not happy. I don't want to go there any more."
- Sports & Recreation