For the Red Devils, meanwhile, their wait for a World Cup final appearance continues, though they will get a chance to better their fourth-place finish from Mexico 1986.
"We are very well organised," Martinez told reporters after the game. "Today is an unfortunate situation.
"The composure in the final third we usually have. Sometimes the ball drops for you – Fellaini had a strong header, we had one on one situations with Hazard. Not scoring the first goal was going to be difficult with the way France are set up.
"My disappointment is huge. It wasn't about having a good tournament and coming top four – it was about trying to win it. It's a sad dressing room now. We could easily have come to this stage and froze. France are used to these big games but we coped with that side really well. We wanted to play seven games, we achieved that. These players deserve to finish on a high."
France have beaten Belgium three times in World Cup matches, more than they have beaten any other side in the competition.