Real Madrid's performances in the Champions League haven't inspired much confidence either, failing to beat Tottenham home and away to finish runners up in their group.
"We did everything we could and there is no explanation for why the ball didn't go in", added Zidane, who signed a new contract to keep him at Real until 2020 earlier this week.
That had never happened before in Madrid's entire history and the sorry stat did not change in this match either. "We can do that in the next game".
Despite all the chances for Real Madrid, Villarreal had a few itself, taking 10 shots four on target.
According to a report by Spanish publication Don Balon, succession plans are already being laid down to replace Zinedine Zidane at Real Madrid, if he is sacked by Florentino Perez.
His players, however, were bright and purposeful from the beginning of this game, and were denied a goal when Bale was deemed to have drifted into an offside position when he nodded home Cristiano Ronaldo's headed assist following a corner.
For the opening 73 minutes of their respective games this season, Villarreal held Barcelona and Real Madrid to a goalless draw.More news: Owen predicts the victor of the clash between West Ham and Huddersfield
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Real were finding it tough to break down the Villarreal defence and introduced Marco Asensio and Lucas Vazquez for the final 20 minutes.
There are problems throughout the Madrid team, with no player scoring more than four league goals, the defence looking nearly constantly vulnerable and the midfield failing to adequately connect the two ends of the pitch.
Kenyan striker Michael Olunga had a day to remember on Saturday as he came off the bench to score a hat-trick in Girona's historic 6-0 win over struggling Las Palmas.
Most shocking at the Bernabeu was a vague feeling of inevitability about how things played out. In football, there are bad runs and we will change that together as a team. Villarreal are a team that likes possession, but we have played a good match in general.
Looking ahead, Real Madrid's search for top form will continue Thursday when they travel to Estadio Municipal de Butarque for the first leg of their Copa del Rey quarterfinal against Leganes.
"We knew that we could make history today and we always believed it", said Villarreal coach Javi Calleja.