"We slid slightly wide in a right-hand junction and hit something, a stone or something," said Neuville, who won stage 13 on Saturday. "It pushed the tire off the rim, it deflated and then it was finished. It's not possible to win any more."
Ogier clinched the world title on Thursday when Ford Fiesta driver Neuville failed to win the power stage. The Frenchman trailed by 28.7 seconds after Friday but won five of Saturday's seven stages to make up ground.
Meanwhile, nine-time world champion Loeb earned his 900th career stage win on Saturday.
"It was raining like hell in there, so bad we were aquaplaning," said Loeb, who took stage 10. "It's a close fight now and of course we'll do what we can (to win)."
Loeb has run only four rallies this season. The Citroen DS3 driver won in Monte Carlo and Argentina and was a runner-up in Sweden.
The Rally France ends on Sunday with six stages.