The Spaniard was subjected to jeers from some sections of the Bernabeu crowd during last night's 2-1 home defeat to Atletico Madrid in La Liga.
Casillas was not particularly at fault for either goal, but has seen his position come under scrutiny following costly mistakes at the end of last season and during the World Cup for Spain.
"The public are in charge and if they need to whistle they will. I've got to keep working and respond in the best way I know, which is to play football," he told Marca.
Casillas faces pressure from summer signing Keylor Navas for the gloves at Madrid this season.