Alberto Contador (Trek-Segafredo) attacked and Miguel Angel Lopez (Astana) went after him, eventually winning the stage, but Sky's captain and race leader kept watch on Nibali, lying in second overall.
"We were concentrating on Nibali, he is second in GC," Froome explained. "If Lopez continues like this, we are going to have to respond to his attacks as well. Today, though, it was Nibali."
Froome rode three kilometres down from the summit finish to a sports centre to speak with press and to find his waiting Team Sky bus. Tonight, he and the team fly to the north where the race will continue its third week after Monday's rest day.
He leads the overall by 1-01 minutes on Nibali and 2-08 on Ilnur Zakarin (Katusha-Alpecin).
However Colombian 'Superman' Lopez could start to become a worry for Froome. Today, he jumped from 10th to sixth overall ahead of his team-mate Fabio Aru.
Watch: Vuelta a España stage 15 highlights
"I'm not surprised by Lopez and how strong he's been. He's been extremely consistent over the last mountain stages," Froome added. "I expected him to try again especially with Astana pulling in the stage. They had the objective to win the stag with Lopez. He's ridden a fantastic race."
The stage only covered 129.4km, but included two major climbs, the final to 2510 metres above sea level. Contador went early with Lopez at 26.5km out and Nibali tried later, at 13km to go.
"With the first climb super steep and some fear of an ambush, we were ready for this tricky part," Sky sports director Nicolas Portal explained.
"On the last climb, with Contador attacking and going away, we just paced ourselves. The key thing was not to panic and make sure we didn't blow ourselves up.
"We were not too worried about Lopez, because he was riding for the stage win. It was more about Alberto, but we thought he would pay for that effort. I think we were right to keep riding at our pace."
Sky nullified all the efforts with Gianni Moscon, Mikel Nieve and finally Wout Poels. The major splits only happened in the final kilometre when Ilnur Zakarin (Katusha-Alpecin) attacked to gain time and move to third overall while Contador lost ground.
"It's the end of a very hard block, two very extreme days today and yesterday," Froome said. "I think everyone that had energy already spent it. Everyone was already on the limit.
"We saw some gaps at the end, 500 metres to go. We had gaps in the main GC group. Alberto was dropped in the final everyone gave everyone they had today, there wasn't' much left today for the riders.
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