The under-pressure Real Madrid striker’s goal drought in the international game continued on Friday, as France staggered to a scoreless draw on Friday in Georgia
The last time that the Real Madrid striker scored for his country was on June 5, 2012, against Estonia, when he netted twice in a friendly leading up to that summer's European Championship.
It has since been 15 games without a goal for Benzema - and just three in the last 27 for les Bleus - prompting the French sporting chief to speak out against the forward.
"There is a problem," Le Graet told reporters. "He is very disappointing. A starter at Real Madrid can't be as bad as people say. We expect more."
Benzema, who was withdrawn in the 62nd minute against Georgia in favour of Andre-Pierre Gignac, jumped to his own defence after the match, suggesting that he is not the only player failing to find the back of the net amidst France's five-game goalless drought.
"I know when I am good or not," he told reporters. "[On Friday]I was not terrible. For me to do better in the next game, I will not dwell on my substitution.
"It’s complicated - we don't win, we don't score goals and we don't do good things. It's a difficult period. I wouldn't say we doubt ourselves but it's becoming a long time since we scored a goal."
The scoreless draw essentially locks France into second place in their World Cup qualification group behind Spain, meaning that they must advance through the play-offs, a fact with which Frank Ribery seems content.
"It's a shame. The opportunities are there," the Bayern Munich winger told reporters.
"We had a lot of chances in the second half. We just didn't score. We are disappointed. We will get back to work and we will recover well because play again on Tuesday.
"We should not think we are already eliminated. If it is necessary to go through the play-offs, then we will. We will win and we will qualify for Brazil."