Didier Deschamps's men crashed out of the tournament in the last eight as they fell to a 1-0 defeat to Germany, as Benzema and his fellow attackers failed to break down the resolute backline of Die Mannschaft.
"We are disappointed that the adventure stops there. We gave everything, but we couldn't score," he told reporters.
"The first period was quite difficult, we didn't have enough attempts for my taste. We had more in the second half, they were endangered, but they have a very good goalkeeper."
Benzema scored three goals in his five matches at the tournament.