Two years after losing the 2006 World Cup final to Italy on penalties, France failed to reach the knockout stage at the 2008 European Championships.
They suffered the same blow at the 2010 World Cup, where the players shocked the world by boycotting training to support Nicolas Anelka after the forward was kicked out of the squad for insulting then coach Raymond Domenech.
With France trying to restore their reputation, they cannot afford another exit, M'Vila told a news conference at the Clairefontaine training camp.
"It would not only be a failure, it would be a complete disaster," the Stade Rennes midfielder said.
France's players have learned to be cautious about the country's prospects at major tournaments but M'Vila, who is heading for his first major finals with Les Bleus, was more optimistic and said their only aim was winning the title.
"We go to the Euros to make it [a] victory," he said, adding that France should be much higher than 16th in the FIFA world rankings. "We're more a top five team," he said.
France are in Group D and play England on June 11 before facing co-hosts Ukraine four days later and Sweden on June 19.
