The three-time world champion came to London as the overwhelming favourite but failed in his bid to become the first Frenchman to win the Olympic sprint title in 40 years on Monday.
He lost 2-0 in the best-of-three final to Jason Kenny of Britain, an opponent he had always beaten in the past.
The British team has already won five out of seven possible gold medals in the track cycling events in London. If Britain sweeps all three remaining events, it would surpass the seven golds it won at the Beijing Games.
Bauge, who had been in a class of his own this season, used the post-race press conference to ask Kenny to explain how he prepared for the Olympics.
"It's not like we did anything different," Kenny answered. "The Olympics was our main goal and objective. As an athlete, we always try hard and when you get to an Olympics that's when all our training comes together."
Earlier this year, Bauge blew apart a field of rivals including Kenny at the world championships, where he didn't lose a single leg in his sprint matches.
"The English don't have the same approach," he said. "We, the French, we can't sacrifice a world championships because there is the risk to vanish completely (from the media attention). Now it's time to ask ourselves the good questions. We have results at the world championships and on the biggest stage we end up runner-ups."
Known for his raw burst of speed, Bauge could not match Kenny's pace on Monday, less than five months after defeating him in the match for the world title.
"So if I understand you well, for the next four years you will just relax and then when it comes to Rio, you'll be on top again ... And Bang!" Bauge told Kenny.
Kenny inherited Bauge's 2011 world sprint title after the Frenchman was stripped of his gold medal for violating rules on rider availability for drug tests for one missed test in 18 months.
The British rider said the fact that the Olympics were held in London this year gave his team an extra motivation.
"The Olympics is the main one for us and I think that's the one we put the most into," Kenny told Bauge. "But me, personally, I still want to win at the world championships, it means a lot to me."
The 27-year-old Bauge, who hinted before the Games that he might end his career after London, said "small details" gave Britain the edge and praised their approach to competition.
"They surely know how to raise their level. But I was laughing on the podium because I can figure out what's happening," Bauge said. "It's been the same story for the past three days."