The striker spent an isolated evening in attack at the Donbass Arena as his team could only manage one shot on target all game. Laurent Blanc's men succumbed to La Roja's possession and high-pressing football and Benzema said his side failed to cope, although he pointed out that their opponents were equally restricted in front of goal.
"If you look at the whole game, Spain had one chance, one penalty and that's about it," Benzema told RMC. "There are always regrets after a game.
"Every team that plays against Spain does not see the ball. You have to stay at the back and wait for a counterattack. That is their style and it is the way it is, very tough. Besides they pressure you a lot."
Despite the exit, Benzema acknowledged that les Bleus had enjoyed a fruitful tournament following early group-stage eliminations at Euro 2008 and the 2010 World Cup.
"This team have a future. We bow out of the tournament with our heads up, knowing we can only be proud of what we did. We reached the quarter-finals, it is nice."
His team-mate Yohan Cabaye also believes that France are on the right path after recovering from the debacle of the 2010 World Cup in South Africa.
"We must not overhaul the entire squad, but just keep working together," he told L'Equipe. "We have built something."
France meet Uruguay in an international friendly in August before kicking off their 2014 World Cup qualification campaign in Finland on September 6.