Cristiano Ronaldo was out of sorts as Real toiled in the rain at the Bernabeu, and the forward was left aggrieved when he was denied a penalty after a trip from Mario Gaspar late in the first half.
Real Madrid versus Villarreal kicks off at 16:15 local time at the Santiago Bernabeu on Saturday and, due to boadcasting laws in the United Kingdom, it can not be shown live at that time.
The master scene in the game was three minutes before the final whistle when Villarreal midfielder Pablo Fornals scored the only goal in the game and secured the three points for his team.
"There is no explanation for this", Zidane said. The hosts pulled one back in the 88th minute through Florin Andone and Adrian Lopez had a gilt-edged chance to level in stoppage time but smashed the ball into the stands.
"It's a hard moment for us". But apart from that we had a good game, and they did what they had to do'.
"We didn't deserve this result".
"It's hard, but nowadays everything that is said about Real Madrid is negative, and I don't see it that way, we're not that bad", he told reporters.More news: Martha McSally, Arizona Congresswoman Tells Republicans To Grow 'Pair Of Ovaries'
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"Today was a hammer blow but we are going to turn things around on Thursday [at Leganes in the Copa del Rey]".
They could fall a gaping 19 points behind runaway leaders Barcelona if Ernesto Valverde's side beat Real Sociedad on Sunday.
Villarreal moved to fifth place with the victory, its first ever at the Bernabeu.
Marcelo added: "It is how it looks from the outside - we are sad, angry and we feel like we are sinking".
Cristiano Ronaldo was thwarted from close range on the stroke of halftime by a breathtaking save from Villarreal goalkeeper, Sergio Asenjo.
Gareth Bale is the only La Liga player to have scored four or more goals this season after playing fewer than 500 minutes (498).
Fornals provided the moment of the half when his exquisite through-ball foxed the Real defence and reached Carlos Bacca, but the Colombian was squeezed out by Keylor Navas. Fornals picked up the loose ball just outside the area and chipped it over the goalkeeper for the stunning victor.