Asked about his team appearing to lose their way in the game in the second half, Solari said that he felt Real had been in control but unable to take advantage of the space Villarreal left behind as they pushed up for an equaliser.
Real soon seized the lead via a couple of quick goals from Karim Benzema ('7) and Raphael Varane ('20) but sure enough it was Cazorla who rescued a precious point for the Yellow Submarines with an 82nd-minute effort to complete his brace.
He said, "We are disappointed, we did not have to draw today, we had chances to finish the match, we did not".
"We had the lion's share of possession, we controlled the game in many moments and we into Villarreal's box more than they did ours".
Real are now fourth in the LaLiga table, eight points behind Barcelona, taking on the Yellow Submarine on Thursday before hosting Real Sociedad on Sunday.
The three-time reigning European champions open the day trailing first-place Barcelona by eight points and will hope to close the gap.
"We started off badly with an error and a goal, but then we got back into it". But it's true we were lacking clarity in our breaks, and missed players like Gareth who are specialists at that.
The 23-year-old has played an important part in Madrid's form of late and their succes in the Club World Cup before Christmas, but they will now lose their young midfielder for the games against Villarreal, Real Sociedad, Real Betis and Sevilla in the league. Now we need to keep working hard and rack up some points.
Villarreal receive Madrid in the relegation zone, but know that a draw will be enough to lift them above Athletic Club on goal difference.