Despite racking up 26 shots, Real were well below their best and look a shadow of the side that won a Liga/Champions League double last season.
Fornals struck with three minutes left to leave Zinedine Zidane's wasteful side fourth and nearly certainly leaves the defending champions out of the title race.
Los Blancos failed to eat into that massive gap after a sublime finish from Fornals scored for the visitors, who had Asenjo to thank for a number of vital saves.
"We're trying to play good football, to move the ball around and score goals but it's not coming off".
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He said: "Sixteen points is very far away and now isn't the time to think about anything other than the next game. In hard moments we need the fans to be on our side".
'We have to be smart in our judgement because they are the same players, the same trainer and the same philosophy'.
Fornals 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.
The fact that the defeat came courtesy of an eighty-seventh minute goal though, was like a dagger through the heart.
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"We have to show on the field that we are improving", said.
Real are fourth in the LaLiga standings on 32 points - one point ahead of Villarreal and eight adrift of third-placed Valencia, who beat Deportivo La Coruna 2-1 on Saturday.
Florin Andone headed in a late consolation for the home side with three minutes left.
Goncalo Guedes tried his luck with an angled effort from 20 yards, which squirmed under the keeper at the near post and rolled into the net.
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