France trailed 1-0 at half-time in Gomel, Belarus, on Tuesday but, after a heated speech from Evra, the visitors took control in the second half of the World Cup qualifier to triumph 4-2 on the back of a Franck Ribery brace.
Evra was stripped of the captain's armband in 2010 following his involvement in a players' revolt against then-coach Raymond Domenech at the World Cup in South Africa.
But despite his demotion and the fact he was only on the bench in Gomel, the 32-year-old left-back delivered what team-mate Ribery labelled 'a man's speech' at half-time, which earned praise from Le Graet.
"I was not there, however I heard that Evra, even if he was not in the starting line-up, was very close to his team-mates at the half-time break and spoke to them," Le Graet said on Wednesday.
"He reassured them, which is the most important thing in these moments.
"Then, (head coach) Didier (Deschamps) changed the system after the break."
While Le Graet emphasised the positive nature of Evra's address, Ribery made it clear there were not many nice words involved.
"We had a real talking to from Patrice Evra at half-time which did everyone a lot of good," Ribery said.
"It was a man's speech.
"He told us that if we wanted to make second place, we had to show a different face."
The win in Belarus ensured France will at least finish second in UEFA's Group I of World Cup qualifying, which will earn them a berth in a two-legged play-off versus one of the other second-placed teams in European qualifying.
The team talk from the Manchester United man also underlined the guidance provided by Evra, who goalkeeper Hugo Lloris labelled 'a real leader'.
Le Graet described Evra as 'a great man', while he also blamed 'so-called sports specialists' for the United defender's reputation as a troublemaker, despite the fact the veteran was suspended for five games by the FFF following the revolt in South Africa.
"Apart from what happened a few years ago, we know Evra loves the national team," Le Graet said.
"He is a winner. He is a regular with Manchester United. He captained the team as well.
"It's nothing. He just has this bad reputation, aggravated by some so-called sports specialists but he is a great man.
"He has the national team in his blood and he wants to do well."
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