Real Madrid also suffered one of their most embarrassing losses of the season when Barcelona thrashed them 3-0 at the Bernabeu last month.
They were the far more active side, holding 56 percent of possession and having 18 shots compared to Villarreal's four, but they couldn't find the finishing touch despite several close calls-including Gareth Bale being ruled offside after finding the net off a corner and Cristiano Ronaldo hitting the outside of the post.
They are now fourth in La Liga on 32 points, 16 points off leaders Barcelona who can stretch the lead with a win away to Real Sociedad on Sunday. Real Madrid president Florentino Perez is notorious for lacking patience when it comes to keeping managers after trophyless campaigns, and Zidane could be the latest one to fall prey to the policy.
Zidane's side dominated the game but succumbed to an 87th minute strike from Pablo Fornals, who chipped over goalkeeper Keylor Navas on the rebound after a lightning quick counterattack, giving Villarreal their first ever win at the Bernabeu in 19 visits in all competitions.
Zidane, 45, has won La Liga, two UEFA Champions Leagues, two FIFA Club World Cups, one Spanish Super Cup and two UEFA Super Cups since taking the top job at Real in January 2016.
"We did everything and there is no explanation as to why the ball didn't go in", he said.
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He told reporters ahead of Saturday's game with Villarreal: "We can't always look at or listen to what is being said".
"We have to be smart in our judgment because they are the same players, the same trainer and the same philosophy", he added.
Much of the credit on Saturday must go to goalie Sergio Asenjo, who will go down in Villarreal lore for his performance in goal.
"We are hurting from this blow, but we are not going to change our mentality, to move forward, and to fight". We must keep working hard and win some games.
Asked about his players' mentality, Zidane conceded confidence is low. Villarreal still looked unsafe on their rare forays into the opposition half and Nacho did well to deny Bacca a clean shot on target with a well-timed block.