Earlier in the season Mourinho criticised Gijon for the side they fielded against Barcelona, with Preciado suggesting last week that had the Portuguese still have been coaching in England, his comments would have seen him "thrown in jail."
The over-hyped build-up made for a hostile atmosphere in Gijon on Sunday night, with Real eventually taking the win through Gonzalo Higuain's late goal.
"The game was complicated for many reasons, such as the comments made before the match, the atmosphere at the stadium," Casillas said.
"We stepped up to the challenge and earned three vital points. In all fairness the atmosphere was hostile. The home crowd supported its team 100%, which is normal.
"We responded well to that. Regarding what was said, I limit myself to defending my coach. I respect other opinions, but I do not share them. I stand by my coach, who is the best."