Goals from Raphael Varane and Antoine Griezmann sent Didier Deschamps' side into the last four with a 2-0 win at Nizhny Novgorod Stadium.
Tabarez has been in charge of Uruguay since 2006 but suggested his time at the helm could come to an end in the wake of their departure from the tournament in Russia.
"I don't know any examples where the coach decides who will be the coach in the future," he told a news conference. "I have a contract, but I won't speak about this. It's not up to me to decide.
"I've never liked to comment on this and I won't do it today. If I did, I'd be going against my principles. This phase is over, the same happened after the World Cup in Brazil and it was decided later if I would continue."
France benefitted from a dreadful error committed by goalkeeper Fernando Muslera, who parried Griezmann's second-half strike into his own net to put the match beyond Uruguay.
Tabarez, though, refused to blame his players for what he accepted was a fair result.
"I won't tell you what I discussed with my players," he said. "It wasn't a normal goal but Muslera has been a very important pillar of our process. I won't wash my hands and put the responsibility on the players.
"We didn't play as well as the opposition, and that's why we lost. When I say 'we', I really mean the whole team. It's not just the team on the pitch's responsibility. We've always believed that.
"We made a huge physical effort in the first 20 minutes, but we couldn't exploit France's problems after that. Then they scored and that's a detail that has a huge impact on a match like a quarter-final.
"The boys gave everything, but France controlled the match very well. After the second goal, there was a big gap between the teams. We couldn't control their strengths and they were better than we were, I admit that."