After spending the day in a five-rider breakaway during stage 12, the 28-year-old Frenchman came within metres of winning his first Grand Tour stage before the galloping peloton swept past and ushered 22-year-old Danny van Poppel (Trek Factory Racing) in for the win.
Bouet crossed the line in 57th place, clearly distraught after watching the stage win slip through his grasp at the last possible second.
"I am the kind of guy who likes to try and attack," he said later. "However, today it hurts a little bit when it doesn't work out."
Bouet, who was second in a stage of the 2010 Tour de France to Sylvain Chavanel, joined Miguel Ángel Rubiano (Colombia), Jaco Venter (MTN-Qhubeka), Bert Jan Lindeman (LottoNL-Jumbo) and Alexis Gougeard (Ag2r-La Mondiale) in a move that escaped early in the 172.5km transitional stage from Andorra to Llieda.
Although conventional wisdom called for a sprint finish, the escapees enthusiastically played their cards, while race leader Fabio Aru's Astana team kept them in check.
"They didn't give us much room," Bouet said.
As the finish neared, Trek and Giant-Alpecin moved to the front for their sprinters and started to close down the gap, but the breakaway riders refused to concede their chances.
"In the last 30km we really went full gas," Bouet said. "When they told us at about 18km to go that we still had two minutes, I started to believe in it and how I would play the final."
The gap seemed enough on the flat roads outside of Llieda, but it began to come down dramatically under pressure from the sprinters’ teams. The closing chase spurred attacks from Bouet and Gougeard, but it was Venter that managed to gap the rest inside the final kilometre.
Bouet regained contact with Venter and then slipped past, but the peloton could see they were fading and was soon on them up the slightly rising finishing straight.
"When Alexis Gougeard attacked I followed him, I knew he was a dangerous guy in a final like that," Bouet said. "Then in the last kilometre when Venter attacked, I let him go a little bit and used him as a point of reference. I caught him and tried to go to the finish in front.
"I tried to not look back," Bouet said. "I had a feeling the peloton was catching us, but I gave everything. In the final few hundred meters or so they caught me. Unfortunately, I was a few hundred meters short today."
Bouet expressed disappointment for himself and for his team, which has been aggressive throughout the first 12 stages – earning the red number of the day's most aggressive rider three times – but Etixx has no significant result so far to show for the effort.
"We probably deserve a nice result after almost two weeks of fighting," Bouet said. "Let's see what the next stages can bring. The fight is not over. I feel good, so why not? We will try again. We always have a plan every day to try and go into the breakaway and go for good results while also protecting the placement of [Gianluca] Brambilla.
"I think from tomorrow on, one of the guys can make it," Bouet said.