Marseille have not won in the top flight at Bordeaux since 1977 and the latest loss left them eight points from third place, the last qualifying spot for the Champions League.
"We must stop looking for excuses," the French international was quoted as saying by French media on Saturday.
"For a podium finish, it's over. Let's stop lying to ourselves, we didn't have a good season and even if we managed to go to the Champions League, what would we have to show? Here we are, it's the same every year."
Marseille have not played in the Champions League since the 2013-14 season.
"We just have to shut up and acknowledge the fact that we're useless. We were useless, we have to admit it," said Thauvin.
Marseille are fifth in Ligue 1 on 48 points with seven games remaining.