Real fans whistled at coach Ancelotti and goalkeeper Casillas at the Santiago Bernabeu a week after the 4-0 derby hammering against Atletico Madrid.
Ancelotti took that on the chin, though, after goals from Isco and Karim Benzema secured a win which moved the European champions four points clear of second-placed Barcelona, who play Levante on Sunday.
He said: "It's normal for me or the team to be whistled. It's frustrating for everyone to lose a derby 4-0. We all understood the need to win and the importance of the support.
"We need to say thank you to the fans. It's hard to support the team when things go badly. The team are grateful for it."
The Italian added: "Casillas whistled? As always, the whistles were at the start and then they stopped and there was applause for the game he had."
Cristiano Ronaldo and Gareth Bale struck the crossbar, but Real did not have things their own way and Depor midfielder Celso Borges rattled the post in the second half.
Ancelotti added: "It wasn't an easy game. We only played well in parts and we had tough spells. The week was different, delicate, complicated, but we came out of it with a win.
"Today we did at times what we always do. There were worries, but everything turned out alright. The fans helped us. They helped us come out of this."
Ancelotti also allayed concerns over Marcelo's fitness after the defender was withdrawn due to injury late on, revealing that the Brazil left-back will be fit to face Schalke in the UEFA Champions League on Wednesday.
