Despite Team Sky setting a searing pace on the final climb, Contador (Tinkoff-Saxo) attacked with two kilometres to go, dropping Froome inside the final kilometre.
"I noticed that some of my rivals were in difficulties and I wanted to use the opportunity. I still lack condition to keep the pace at maximum intensity, but I'm very happy," said Contador who could not drop Nairo Quintana (Movistar) and Joaquim Rodriguez (Katusha).
"Whenever I have the legs, I have to try. I haven't been able to prepare properly for the Vuelta to ride for the GC as a goal. I hope to improve day-by-day, but I'm aware that there are other riders, who have been training meticulously ahead of this race. Perhaps today they didn't have a good day, but the Vuelta has just begun."
Froome eventually finished 19 seconds behind Contador, crossing the line with overnight leader Alejandro Valverde (Movistar) and other general classification contenders Rigoberto Uran (Omega Pharma-Quick Step) and Fabio Aru (Astana).
The Team Sky rider now sits fifth overall, 28 seconds behind new race leader Quintana. Contador trails Quintana by just three seconds, with the top four now separated by a mere nine seconds.
Despite the time loss, Froome remains optimistic with two weeks remaining.
"Conditions were really tough out there," said Froome.
"I think we can take a lot of good away from that stage in terms of how we rode as a team. I'm so so proud of how the guys rode today, they did such a good job. They kept me at the front throughout the stage.
"In the final I didn't have the legs to follow the top guys when they went. But I think given where I've come from on the back of the Tour and the build-up into the race I'm really happy with how things have gone so far. I can definitely feel I'm starting to pick up that race rhythm back into my legs and I'm looking forward to the second half of this race."
Froome hopes his time trial skills will help him to claw back time in the 36.7km time trial on Tuesday.
"I'm going to go and see the time trial course tomorrow and see what we're up against. It's relatively short compared to time trials elsewhere. But I enjoy time trialling and I'm hoping to make the most of it.
"I think we've come to see that Contador is going extremely well. He's got over his injuries pretty quickly and he's going well, as are Nairo Quintana and Rodriguez. The usual guys we expected for the general classification. It's a huge fight here and it's going to be a big race all the way to the end. Every second here or there is going to count."
SBS will broadcast eight live stages of the Vuelta a Espana, in addition to daily highlights.