An injury to the Spain skipper in January forced the signing of Diego Lopez as cover but, with the 31-year-old having recovered, the former Villarreal man's form has confined Casillas to the bench.
However, Del Bosque, who spent 14 years as a player at the Santiago Bernabeu as a player and enjoyed three spells there as a coach, says everyone associated with the club should be grateful to the goalkeeper.
"A good Madrid fan must love Casillas a great deal," he told Colombian radio station W Radio on Tuesday. "Like Casillas, we are sons of Real Madrid, the club that made us."
Mourinho is said to have a bad relationship with several of his players and Del Bosque feels it is natural that Casillas would prefer working with other bosses.
"Everyone is entitled to their own opinion and Iker is within his rights to say he prefers Del Bosque or [former Madrid boss Manuel] Pellegrini as coaches," Del Bosque explained.
Mourinho said earlier in May that he wishes he had signed Lopez sooner than the most recent transfer window, hinting that he will continue to choose him ahead of Casillas but the former Inter boss is set to return to Chelsea.