Dumoulin was one of the strongest on the brutal 16km climb of the Col du Portet, but an attack from Thomas distanced him close to the line and he lost a further nine seconds.
When asked if he was now in a race to keep second he said: “I always keep a little bit of faith, a little bit of hope I can win. But so far over the two and half weeks Thomas has been the strongest. So far, I’ve not been able to get time on him – that’s it.”
The Dutchman climbed off his bike and collapsed against the barriers to catch his breath after reaching the summit of the Col du Portet. He now has only two stages, a mountain stage on Friday and a 31km time trial on Saturday, to make up 1-59 on Thomas.
Dumoulin, who also raced the Giro d’Italia in May and finished second, said he didn’t think too much on the day’s final climb: “I was thinking pain. That was pretty much it,” he said.
“The first attack of [Primož] Roglič in the final I saw that [Chris] Froome was in difficulty but I was blocked so I waited a little bit. I went and tried but I didn’t have the legs to drop Thomas and Roglic. At the end I stayed with Roglic but Thomas was just the strongest.”
Asked if he still considered Froome a threat to the overall win, Dumoulin was sceptical.
“Of course yes, but it’s going to be difficult because his team-mate is in yellow and he’s definitively the strongest in the Tour. I don’t see Froome winning in a hurry,” he said.
“But you never know what can happen, look at the Giro. I focus on myself, not Froome.”
He added: “It could be that Froome did last year’s Tour and Vuelta, maybe it’s a bit too much.”
The Sunweb captain was left isolated for big chunk of today’s 65km stage, while Froome and Thomas had four team-mates with them at the start of the final climb, he had none.
He was hardly alone in that respect, Romain Bardet (Ag2r La Mondiale) had only one team-mate with him and while there where three riders from LottoNL-Jumbo, two of them are mounting GC challenges. Sky outnumbered all other teams by a considerable margin.
But Dumoulin didn’t think his lack of team-mates had hurt his chances.
“With a stronger team the outcome today would be exactly the same,” he said.
“But it’s true that if something happened like I had bad legs and didn’t have anyone to pace me it’d make a difference but if I stay strong, that’s it.”
Sunweb sports director Luke Roberts said that it appeared increasingly difficult for Dumoulin to beat Geraint Thomas.
“Thomas isn’t in reach if he rides like he did today,” he said. “If he keeps that up. The way Thomas is riding yes it’ll be hard to bet him.”
While Roberts was satisfied that his rider had managed to split the Sky pair and climb another step up the podium he said he was expecting a further shake up on Friday.
Asked if there was a plan for the stage Roberts smiled. “There’s always a plan it is a difficult stage,” he said.
“It’s a bike race on Friday. It’s a tough stage with the Col du Tourmalet and the Col d’Aubisque its two brutal climbs it could be a different outcome to today.”