Mourinho dropped goalkeeper and captain Casillas, which caused controversy even before his side slid to their fourth Liga defeat of the season.
That put the defending champions 16 points behind leaders Barcelona, as well as publicly highlighting the divide between the Portuguese coach and his Spanish stars.
Mourinho said that his decision to drop Spain goalkeeper Casillas for the first time in a decade was “technical, not personal”, although there have been reports of disagreements between the two, and defender Sergio Ramos.
"We are facing an insurmountable gap,” Mourinho added. "Football is football, why should I fear for my job?
"We coaches know perfectly well that football has no memory. The titles you have won don't count, the work you have done doesn't count.
"Losing always hurts but it hurts me more when you don't give what you are able to give.
"In the brief chat I had with the players I told them they can go home sad at losing but in the knowledge that they did their job to the best of their ability."
Madrid are still in the hunt for the Champions League, although they face Premier League leaders Manchester United in the first knockout phase in February.