The world number two lost 6-4 6-2 to the Spaniard, who was clinical in reaching the semi-finals of the BNP Paribas Open.
Federer suffered a recurrence of a back problem earlier in the tournament, but said that he did not want to draw too much attention to it.
He also said that Nadal looked comfortable following his return to hard-court tennis after a long layoff with a knee injury.
"The longer the match went on, I realised I had to change up my game," ESPN quotes the Swiss as saying. "I played differently than I was hoping to be able to. He got more comfortable as the match went on.
"Obviously, once I was down a set I knew it was going to be difficult.
"You could see at least I could serve full basically, and that always gives you a direction. I don't like to undermine his performance, either."
Nadal will now face Tomas Berdych in the semi-finals.