Pogacar, who crashed early in the stage and lost one minute and 38 seconds in Tuesday's individual time trial, trailed overall leader and defending champion Jonas Vingegaard (26) by 1:48 going into the toughest stage of this year's race.
As a reduced peloton tackled the steep part of the 28.1km climb, Pogacar zipped open his jersey and dropped out of the group, getting into UAE Emirates team mate Marc Soler's (29) slipstream.
"I'm gone, I'm dead," an out-of-breath Pogacar said in his team radio as yellow jersey holder Vingegaard was disappearing in the distance.
Pogacar, flanked by Soler, crossed the line more than five minutes behind his rival to end up a massive 7:35 behind the Dane in the overall standings four days before the parade on the Champs Elysees.
He spent a few minutes slumped on a chair before saying: "I came to the foot of the climb totally empty. I ate a lot but it didn't come to my legs. I'm extremely disappointed. It was one of the worst days on a bike in my life."
It was the day when Pogacar was expected to strike back after being humiliated in Tuesday's solo effort against the clock, but it quickly appeared he would struggle to deliver.
A few kilometres into the stage, the Slovenian crashed after touching wheels with another rider and sustained a cut to his left knee.
"It was a really unlucky situation. It was on a climb and the guy in front of me slowed down and changed lines and I touched his wheel," a dejected Pogacar said.
He is, however, already looking ahead, hoping to win Saturday's penultimate stage, a hilly trek that favours the attacking riders.
"If I recover from today yes, I want my team to get a stage win, we'll try for Adam (Yates), anyone from the team. If someone can win we'll try it. I thought about that at the start of the climb."
Briton Yates is still third overall, 10:45 off the pace and with a 1:16 lead over fourth-placed Carlos Rodriguez (22) of Spain.
Pogacar might have paid a price for his repeated attacks earlier in the race, and hampered preparations after fracturing his wrist in April.
"When you always go on the attack you, make yourself vulnerable and then it's easier for the other one to make a big difference," Vingegaard said.
