A first-half free-kick from Ergys Kace condemned Les Bleus to a second loss in a week after they were beaten 4-3 at home to Belgium last Sunday.
It is the first time that the Euro 2016 hosts have suffered back-to-back defeats since June 2013, but Evra was unimpressed with all aspects of the performance.
“We represent a country. You can mess up a pass or a touch but you can’t lack desire,” said the Juventus defender.
“We got into the habit of working hard at the World Cup, we showed a good side to the French people, desire and respect for the shirt, and we have lost all that in recent matches.
Evra, who was stripped of the captaincy after the fiasco of France’s 2010 World Cup campaign, added: “We must not hide, we must accept the criticism because it is deserved.
“Sometimes we don’t know how lucky we are. How many players would like to be in our place?
“Some people will see that it was hot, that it was Albania, but it is a lack of respect to the French national team.
“We have got a bit too comfortable. I am not worried but we need to watch out. The Euros are in one year, not four. We need to shut up and get down to work.”
France manager Didier Deschamps rotated his squad for the match but was left “angry and disappointed” with what he saw.