The result means that Zidane's side are now without a win in three league games - a run that included a 3-0 humiliation at home to El Clasico rivals Barcelona just before Christmas.
"We don't deserve this," Zidane told reporters after the game. "I think we played a good match. It's very difficult for the confidence We had chances to score but in the end... we couldn't avoid the counter and... it's just very fucked up for all the players.
"What we have to do is keep working, because there will come a time and we have to be there. Within all the negative things that are happening to us, we are going to look for something positive.
"We have to get a win from somewhere. We know the situation and every day it gets more complicated, so we are not even thinking about the league, just about the next match."
Next up for Madrid is a trip to Leganes in the Copa del Rey on Thursday night, ahead of a home encounter with lowly Deportivo La Coruna in the league next Sunday.