Garmin-Sharp riders, soon followed by the Movistar and Saxo-Tinkoff teams, attacked relentlessly in the first of five climbs on the 168.5-km ninth stage in a bid to isolate Froome.
The plan worked as the Briton was quickly without a team mate and left to fend off attacks on his own.
"Since the beginning we saw that Sky were in difficulty," Ireland's stage winner Dan Martin, one of the early attackers, told a news conference.
Although Froome eventually escaped unscathed in the overall standings, still leading Spain's Alejandro Valverde by 1 minute 25 seconds, the moves knocked out Sky's Belarussian Vasil Kiryienka, who was eliminated from the race after finishing outside the time limit.
"It's a huge thing," said Froome.
"He's one of the big engines in our team, we're going to miss him in the next couple of weeks."
Kiryienka was one of the riders with the task of setting the tempo in the climbs, which he did perfectly on Saturday.
Sky also had an early fright when Peter Kennaugh fell off his bike and into a ditch but the Briton recovered quickly.
Australian Richie Porte, second overall at the start of the stage in St Girons, was rapidly dropped and, after almost making contact with the lead group again, cracked to finish 17 minutes and 59 seconds off the pace on the ninth stage.
He is now outside the top 30 overall and has lost all hope of a podium finish in Paris, which was one of Team Sky's tactical goals.
"Definitely it's always better to have two cards to play in that respect and having Richie in second place was a huge boost," said Froome.
"For me, that he was right there and could at any point put other riders under pressure was great. It leaves us a bit exposed."
Froome, however, never panicked.
"I wasn't completely on my own, I had (sports director) Nicolas Portal in the car talking to me," he said.
Sky team principal Dave Brailsford said they could not take the race for granted.
"Last night, everyone was saying 'game over, let's go and watch the tennis,' but no one knows what's around the corner."
With two weeks and a gruelling few days in the Alps left, Froome could be worried. He is not.
"I don't think it helps to worry about things. We're here with what we've got," he added referring to the yellow jersey.
- Sports & Recreation