The Yellow Submarine went ahead early from a well taken strike by former Arsenal man Santi Cazorla's but Karim Benzema restored parity before Raphael Varane headed Real into the head.
However, Bale left at half-time with another calf muscle problem, which saw Real change their tactical approach to a more conservative approach and Cazorla popped up in the dying minutes with a brilliant header at the far post.
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 had the victory in our hand and wanted to kill the game," Solari said, as per ESPN FC.
"But they came back and got the equaliser. They pressed a lot, were playing at home and needed the points.
"Gareth leaving like that cost us as he had a problem and we missed that counter-attacking edge, and Gareth is a specialist at just that. He got a bang in a challenge with the defender, and felt something and was not able to continue."