The Spanish champions have endured a difficult start to their title defence, currently sitting 11 points behind league leaders Barcelona in the Spanish top flight.
"People can think what they want,” Callejon told reporters.
"We're Mourinho's team to the death, he is the ideal coach for Real Madrid. The public can think what they want and you can also think what you want."
The 25-year-old went on to say that he was pleased to have played in a side that contained six home-grown talents.
"It was a good game, we won 3-0 and we enjoyed the people who came to the stadium to support us today. Additionally, to have played with several home-grown players; it was a good night."
Callejon netted a late double to add to Angel Di Maria’s opener against Alcoyano.