Their overall hope, Giro d'Italia winner Ryder Hesjedal, had to abandon because of his injuries.
Millar has also endured a tough season so far and nearly did not start the Tour because of a stomach virus, which had him quarantined in his hotel room for three days.
"We took him at the last moment ... and had faith in him and he's shown his leadership in the race," Peiper said.
Peiper then had to stop as his voice cracked.
"I don't cry - it's just new age," he joked.
Peiper said of the team: "We were in battle mode.
"I must say, last week I had a couple of pretty hard days personally because you've seen the aspirations of the team crumble.
"We've come out day after day trying and David had the legs today and pulled it off.
"It's not about saving the Tour de France, this makes it a success."
As Millar lapped up the plaudits, he was mindful of his past.
He made the team for the London Olympics, but only became eligible when the British Olympic Association were forced to drop their lifetime ban for doping cheats.
"Don't stop calling me an ex-doper," said Millar, now a vocal advocate of clean cycling.
"I was doped, now I'm clean. But we shouldn't forget the past. It's important."
Peiper agreed the anniversary of the death of Simpson, an important figure in British cycling history, added to the significance of Millar's win.
"David Millar has also had a battle of a life on its own," he said.
"His winning a stage now in the Tour de France at 35 years old shows what an old warrior he is."
-AAP
