Froome showed scrapes down his right side when he arrived to the Team Sky bus, but the team's early assessment is that his injuries are superficial.
"No one wanted to crash today," Froome said. "It's just one of those things. We always knew the first few days were going to be tricky, to be sketchy, and that's part of the game unfortunately."
"In the last 20 kilometres things went a bit bonkers," Thomas said after the stage.
The team's 21-year-old Colombian Egan Bernal also fell before Froome, coming in in a group at 1-15 with compatriot Nairio Quintana.
"We were right in the front of the peloton, I'd say in the front third, so there wasn't too much more to go," continued Froome. "We were getting some help from the sprinters there.
"That's bike racing. I am not injured in any way, and there is still a lot of racing to come. I just got on the bus but I am feeling OK."
Froome fell twice early in the Giro d'Italia in May early and still went on to win the race. The opening days are often the most stressful until the race hits the mountains – this year coming only on stage 10.
"The first week is always a bit chaotic," Thomas said. "We were in decent position and we missed the main crash, but then Froomey and Bernal had a bit of bad luck.
"It's not ideal, but it's the end of the world, either. He was with Richie [Porte] and Nairo [Quintana] was behind him, so arguably two of his strongest rivals."
Porte and Adam Yates (Mitchelton-Scott) lost time alongside Froome, while Quintana suffered from a bike problem and rolled in further back at 1-15.
However despite the time loss, Team Sky will not be changing their strategy and backing Thomas over Froome.
"It's the first stage, we have plenty of cards, not plenty, but that's why we push G to keep him up there as long as we can," sports director Nicolas Portal said.
"You never know, tomorrow it could be Geraint or someone else [who crashes]. We have to keep both plans, one more guy doesn't change anything. We told him to stay up front. Geraint didn't lose any time.
"But 50 seconds lost, Chris won the GC last year by that much time. It's clearly too early to [change plans] and he's definitely not someone I'm sending home. He's won six [Grand] Tours!"
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