A lone goal from Jose Luis Morales late in the second half was enough to hand Paco Lopez’s men their tenth league win of the season.
Los Blancos passed up the chance to go top of La Liga and are now two points behind Barcelona, who comfortably won against Eibar earlier on Saturday.
Speaking to the media after the game, Zidane revealed he is not perturbed, but insists Real Madrid must be focused as they prepare to entertain both Manchester City and bitter rivals Barcelona in the space of a week.
"Nothing worries me as this is football and these things happen," the French coach said.
"We've had very good moments this season and we can't down tools or let our heads drop because of two results.”
"We have to think that we can take this forward with us with strength, excitement and energy.”
"It's a bad run, but we have to think about next week, when we're playing for everything."
Real Madrid were the better side during the match, but were not prolific as the hosts kept them at bay.
"We feel bad as we got forward a lot, but we lacked goals," Zidane added.
"We started well, away from home, by creating chances, but we lacked goals and that is the most important thing in football."
“In the second half, they went forward and scored. It's annoying because we've dropped five points in two games.
"Next week, we're playing for everything. We have to think about the good stuff that we've done up until now and get back to winning again.
"After those two games, we know that we have to win at home. We're going to do everything possible to get back to top spot, but we have Wednesday's game first.
"We have to try to get back winning again."
