"I'm proud of my team-mates - they were lions," Godin said, as he and his fellow Uruguay players came off the pitch in tears.
"We are a team where everyone gives everything in the matches and in preparation. I have only words of gratitude for my team-mates," he added, as Uruguay's noisy fans cheered them off at the Nizhny Novgorod Stadium despite the defeat.
France won with a Raphael Varane glancing header in the first half and a goalkeeping fumble in the second that gifted Antoine Griezmann a soft goal. Griezmann shot from outside the box straight at Muslera, who attempted to palm the ball away but instead deflected it into the net.
"Fernando is a great goalkeeper ... We all make mistakes," Godin said. "On other occasions he has rescued us with incredible saves."
Uruguay suffered without striker Edinson Cavani, who was ruled out with a calf injury.
France's win set up a semi-final against Belgium.
