Madrid conceded with three minutes remaining as Villarreal upstaged the struggling Spanish and European champion 1-0 at the Santiago Bernabeu.
"We didn't deserve this result".
Zidane's side's Champions League spot for next season is looking perilous - they now sit only one point above Villarreal, who move up to fifth.
It's hard to believe that Real Madrid, the champions of Spain and Europe, are now lying in fourth place in La Liga after 18 games, 16 points behind leaders Barcelona and 10 behind city rivals Atletico, yet Zinedine Zidane's men have slumped from one poor result to the next over the last five months.
Speaking at the Ballon d'Or award, Real Madrid president Florentino Perez said: 'It's hard to see who will take the leadership away from Cristiano [Ronaldo] and [Lionel] Messi.
"We're trying to play good football, to move the ball around and score goals but it's not coming off".
As the home side poured forward in search of a victor, they were caught on the break; Fornals chipping in the rebound after Keylor Navas saved from Eres Unal.
Madrid also had a penalty appeal waved away when visiting defender Alvaro Gonzalez appeared to block a shot from Bale with his arm, while Asenjo made his best save of an outstanding overall display by thwarting Ronaldo from close range on the stroke of halftime.
"We did everything possible to win and I honestly can not reproach my players for their actions".
"That's because 16 points (now 19) is very big".
"Real have many virtues but we thought that at this moment of the season and playing at home, they might make more mistakes".
The fact that the defeat came courtesy of an eighty-seventh minute goal though, was like a dagger through the heart.
Luck deserted Deportivo in the second half when Ruben was beaten again by a Rodrigo Moreno shot which took a wicked shot to leave him totally flat-footed and although Florin Andone scored in the 88th minute for Deportivo, it was too little too late, although Adrian Lopez fired over the Valencia bar when well-placed in injury time.
Kenyan forward Michael Olunga scored a hat trick to lead promoted Girona to a 6-0 trouncing of last-place Las Palmas.
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