Les Bleus were comfortably beaten, courtesy of two Xabi Alonso goals, to see their challenge in Poland and Ukraine end at the quarter-final stage.
"We were not ridiculous," the former Lille man told the French Football Federation's official website. "We have done the essential which was to reach the quarters.
"We knew that in the game, we could win, but we couldn’t quite do it."
France will begin their bid to win a place at the 2014 World Cup in Brazil later this year, and will once again meet Spain, who have been drawn in the same qualification group.
Cabaye believes Les Bleus will be ready to dish out some revenge on Vicente Del Bosque’s side.
“Now we must work for the World Cup and to qualify for this competition. We will have our payback against Spain," the 26-year-old concluded.