All 23 members of the France squad at the tournament were banned from taking part in a recent friendly against Norway. Nicolas Anelka, Patrice Evra, Franck Ribery and Jeremy Toulalan have all been handed further suspensions.
However, Sagna believes France should already be looking to the future.
"It's time to move on," he told Arsenal's Official Matchday Programme. "In fact it was time to move on before [these bans].
"We keep talking about it but it's the past. We should care about building the future.
"We made some mistakes, and we played badly. Everything started because we were bad on the pitch, not because of what was said in the papers. Now we want to move forward. We have to start from nothing again.
"I watched the friendly against Norway and they played well, they played like Arsenal.
"The first half was very good, in the second half there were many changes and they ended up losing [2-1] but the game was very interesting.
"The good thing now is that we can have a completely new start, and think about what has happened, and about what we want to achieve."