Sprint specialist Cavendish, who has 30 Tour stage wins to his name, crossed the line one hour five minutes and 33 seconds after stage winner Geraint Thomas, far outside the time limit that had been set at 31:27.
While he could have stepped off his bike and climbed into the broom wagon, which sweeps up riders falling behind the time limit, Cavendish insisted on finishing the 158-km stage to La Rosiere on his bike.
"Hats off to Mr Cavendish," Prudhomme said to Reuters before the start of the 12th stage on Thursday. "That was such a mark of respect for the Tour."
Prudhomme said he had to press the local authorities not to open the roads to circulation again in order to allow Cavendish to finish the stage safely.
"I want to say thank you to Mark Cavendish. It's such a mark of respect from the best sprinter of the Tour's history," Prudhomme said.
Cavendish had appeared out of form, never being in the mix for the final sprint in the flat stages.
The 33-year-old won his first Tour stage in 2008 and his last in 2016. Only Belgian great Eddy Merckx has won more stage wins on the Tour, with 34 stage victories to his name.
(This version of the story corrects headline to say Cavendish failed to make time cut, not that he pulled out of the race).
(Reporting by Julien Pretot; Editing by Hugh Lawson)
