Yates attacked the group of GC favourites midway in the stage, but when joined by eventual stage winner Miguel Angel Lopez (Astana), he could not stick with the pace.
"I did my best," Yates said. "I can't be disappointed with that. It's a rest day tomorrow, so rest up and try again in two days.
"I slowed down a little bit because I knew [Lopez] would pass me. I tried my best, maybe it was a little bit early when I attacked. I gave it a shot, it didn't work out today, but in the future it will."
Yates, 25, who placed ninth overall in May's Giro d'Italia, attacked with Romain Bardet (Ag2r La Mondiale), Steven Kruijswijk (LottoNL-Jumbo) and Nelson Oliveira (Movistar) with around 60km remaining. He went solo at 25.1km remaining and facing the 2510-metre summit finish at Sierra Nevada.
Only Lopez, who attacked later with Contador, ruined his plans. Yates held on until nearly four kilometres remaining, when the Colombian flew by for his second stage win in the 2017 Vuelta.
Watch: Vuelta a España stage 15 highlights
"There are only so many stages that suit a breakaway that're good for me," Yates said.
"When these other [breaks] go with 40 guys those aren't really good for me because you have to mess about and sprint about 400 times just to get into it, but on a day like today, it's more forced and it suits me a bit better. So we just have to wait until another day like this and try again."
"If I came back I would always be there in a final but when it's like this there's not much more I can do to help him," he continued.
"It's not really about working but just trying to get results for the team. He's in a great position at the moment and we're going to support him all the way to the finish."
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