Iceland, ranked 115 places below their hosts at 131, shocked Les Bleus by taking a two-goal lead through Birkir Bjarnason and Kolbeinn Sigthorsson.
Laurent Blanc’s side reduced the arrears through Mathieu Debuchy seven minutes after the break but they had to wait until the 85th minute to equalise through Franck Ribery before Adil Rami’s late strike won it.
Evra told L’Equipe: “We must not be too hard on ourselves. After one match, you cannot know exactly what you need to do to improve. You can play very well in your warm-up games and lose the first match at the Euros. It is June 11 we must be ready for.”