Karim Benzema equalised with a header and Raphael Varane soon gave Santi Solari's side the lead but Cazorla would have the final say as his 82th minute finish ensured a draw.
With the Welsh galactico having now been substituted 15 times in La Liga this season, more than any other player, Solari lamented his absence.
We chased the victory and had it in our hands.
Villarreal have punched below their weight this season and in strikers Gerard Moreno who scored the only goal as his former club Espanyol beat Madrid a year ago, Carlos Bacca and Toko Ekambi, they have a mixture of height and pace able to cause problems to the Madrid defense. The way they are playing does not make me feel optimistic'. "He got a bang in a challenge with the defender, and felt something and was not able to continue".
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The Blues are now fourth in the Premier League table as they prepare for their home clash against Southampton on Wednesday. I don't think it's a problem of attitude, but more one of impotence. "We had two clear chances for a third goal with Lucas Vazquez and Marcelo. He would have allowed us to exploit the spaces Villarreal left when they pressed up".
"We'll try to play with commitment and energy".
Real Madrid holds the fourth spot in La Liga table with 29 points, eight points adrift of leader Barcelona, a gap that Madrid could narrow to five should it defeat Villarreal in a postponed game due to its successful FIFA Club World Cup campaign.
With Isco in their ranks for the second half, Madrid failed to see the match through and were pegged back by a late Cazorla header to bring an end to their three-match winning streak in LaLiga.