However, politicians and France's football establishment leaped to Deschamps defence over the interview that the Real Madrid star gave to a Spanish newspaper.
Benzema, who is of Algerian origin, was excluded from France's squad after being charged with complicity in an attempt to blackmail France teammate Mathieu Valbuena over a sextape.
But questions about the motives for excluding Benzema and fellow striker Hatem Ben Arfa, whose father was a Tunisian international, have been raised by France football legend Eric Cantona, setting off a new racism debate.
"No, I don't think so. But he bowed to pressure from a racist part of France," Benzema replied, referring to the right-wing National Front.
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"They said I cannot be selected, fine. But on a sporting level, I don't understand why," he said.
"At a legal level, I am still innocent until proven guilty. They should wait until the justice system has made its decision."
The forward said he was "convinced" his suspension was due to outside forces.
And Cantona weighed into the debate again in an interview published on the Liberation newspaper website yesterday night.
When France won the World Cup in 1998 it was hailed as a major step for recognising the country's multi-cultural roots.
However the National Front's rise in recent elections and polls has brought immigration and race back into the political debate.
National Front deputy leader Florian Philippot laid into Benzema on Twitter, declaring: "The French people should not have to put up with your unworthy accusations because you flee your responsibilities."
Mainstream parties also leapt to Deschamps's defence.
Francois Fillon, prime minister from 2007 to 2012,
slammed Benzema's comments: "Forever bringing the nation's problems down to questions of race, religion and ethnic communities, it's unhealthy."
French Football Federation president Noel Le Graet said Deschamps was "blameless" and that Benzema had "let himself go a bit too far".
Rising French star Kingsley Coman called the racism accusations "ridiculous".
"There are a lot of coloured people, or people of different origins, in the team," Coman told a press conference at a team training camp in Austria.
Benzema is France's top scorer with 27 goals in 81 appearances, but even if selected for Euro 2016, it's unlikely he would have been first choice forward ahead of the in-form Antoine Griezmann.
But the race controversy is a blow so close to the start of the tournament in France on June 10.
Cantona originally set off the race debate in an interview with the British Guardian newspaper, saying Benzema and Ben Arfa, who was in fine form for Nice this season, were not in the French squad because of their "North African origins".
Whether Benzema should be allowed back into the France team has been a national debate virtually since he was charged in November.
Prime Minister Manuel Valls and other politicians opposed any return while the sex-tape inquiry goes on. Benzema denies any wrongdoing in the case.