The race leader in red fell off on the descent in the final 10 kilometres of stage, which was won by Tomasz Marczynski (Lotto-Soudal) from an escape group.
Froome appeared as normal when arriving to the press tent, but did not stay around to answer more than three questions as he did after stage 11 at Calar Alto.
"I did come off twice on consecutive corners," Froome explained. "I crashed once, lost my front wheel, crashed. The levers were all bent, I changed bikes right away, went into the next corner and lost my front wheel again. I just carried on on that same bike after that.
"Thankfully, I had my team-mates with me, Mikel Nieve and Wout Poels, they were fantastic and they limited the loses today for me. I am grateful not to be more not to be more injured today, I lost a little bit of skin, but that's the extent of the injury."
Froome still holds the red jersey, but his rivals gained time. Alberto Contador (Trek-Segafredo) took 42 seconds and other favourites, including Vincenzo Nibali (Bahrain-Merida) in second place, took 20.
Froome leads the overall by 59 seconds on Nibali and 2-13 minutes on Esteban Chaves (Orica-Scott). Contador moved to ninth at 3-13.
"It's never nice to crash and lose time like that, but I am just grateful that I had two team-mates there with me," Froome said. "Wout and Mikel were with me all the way to the end."
Froome crashed after Contador launched an attack with with Nicolas Roche (BMC Racing) at around 20 kilometres out.
Contador carried on solo and Sky drove behind to limit his gains. Then Froome crashed on the Puerto del Torcal descent.
The television camera only caught the second one, when Froome was on his own through a right-hander.
"I saw the first crash when he went down in front of me," Nibali said. "The descent was very slippery and very dangerous.
"I kept a few meters of distance because that's my nature and thanks to that I was able to avoid it because I could have crashed as well. It was a curve to the left we were going pretty hard and when you're racing, this is just part of the sport."
The groups had no way of waiting for Froome because Contador was climbing up the classification while riding away solo. They had to continue.
Froome relied on Dutchman Wout Poels and Spaniard Mikel Nieve to pace him back and limit the damages.
"It was a quiet day until Alberto Contador attacked. He did a good ride, and gained some time on all of us," Froome said.
"In danger? Maybe, because the race is not over until we reach Madrid We have to give the best every day now.
"The Vuelta is not over, and there are a lot of big days ahead."
The race continues with stage 13 tomorrow in Tomares, where the sprinters could have one of their few chances in this 2017 edition.
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