While Daniel Martínez (EF) claimed stage honours, minutes up the road, Tadej Pogačar attacked the main group of favourites around two kilometres from the finish, with Primož Roglič hot on his wheels.
Of the top contenders, only Australian Richie Porte hung tough within striking distance of the pair as he left Mikel Landa (Bahrain-McLaren) and the defending champion in his wake.
Although Landa hooked back on and crossed the line with Porte on the same time, Bernal finished 38 seconds behind Pogačar and Roglič, the result moving him down the general classification to third (+0:59).
But Bernal said he can't find the answer to his poor form on the stage by looking at his own power numbers, Dutch news outlet reports.
“I looked at my numbers from today's stage and they were almost my best ever," Bernal said.
“I did my best. But the others were stronger than I was. I couldn't do more than this. I felt very good all day.
"The rest simply went faster."
While the INEOS Grenadiers' had a strong day in terms of the team's efforts to drive the pace on the final climb which hurt riders like Nairo Quintana and Guillaume Martin, their leader said now it's a case of waiting to see what happens, especially with Sunday's big stage to the Grand Colombier.
"From now on I will look at it day by day. We must continue to focus and manage our efforts.
"In any case, I'm not giving up. We have to keep morale high and we do our best."
The 2020 Tour de France continues tonight with Stage 14, a 194km stage from Clermont-Ferrand to Lyon that's for riders who like rolling hills with a bit of speed. Watch the race on the SBS ŠKODA Tour Tracker from 8:55pm AEST and on SBS HD / SBS On Demand from 8:30pm AEST.
