The champions slipped to a second league defeat of their title defence as the home side became the first promoted team to beat Los Blancos in 27 years.
Isco put Madrid ahead inside 12 minutes, but two goals in the space of four second-half minutes undid the visitors and left Zidane's side languishing in third.
The French coach defended the brittle display and affirmed his belief that the title race is far from over.
"We know we can turn this around. We will have better days and the other teams will drop points too over the season," Zidane told reporters at his post-match press conference.
"We lost three points unexpectedly [but] we want to win La Liga, it is our day to day.
"I do not agree that we played badly. All the players made an effort. I am annoyed for them, as it was just details [which cost Madrid].
"We will go home, rest, and get ready for Wednesday. The players are still motivated for La Liga."
1990- Real Madrid have lost vs a newly promoted in their 1st ever meeting in La Liga for the 1st time since 1990 (vs Real Burgos). Stumbling pic.twitter.com/QTbiSmHxOr— OptaJose (@OptaJose) October 29, 2017
"Varane has a small problem with his adductor, that's what I have been told," Zidane said.
"We will have to [wait until] tomorrow [for more details]."