The Portuguese superstar netted either side of the break in a 3-0 win at the Bernabeu as Los Merengues claimed their first La Liga victory of the season.
Ronaldo was replaced by Gonzalo Higuain on 65 minutes after taking a knock to his knee following a late challenge from Borja Gomez, who received his marching orders after picking up his second yellow card.
The 27-year-old forward recorded his 150th goal on the night for Real, but later revealed tension between himself and the club.
“I’m sad because of a professional issue and the club know why,” he said.
“That’s why I didn’t celebrate the goals, because I’m not happy. The people [at the club] know why.
“It’s nothing to do with Andres Iniesta [winning UEFA’s Best Player in Europe award]. I won’t talk about this any more and I will concentrate on Portugal for now. There are more important things [than this].
“The people at the club know about this. I cannot say any more.”