Bilbao coach Joaquin Caparros accused the Real keeper of diving as he made contact with Yeste following the home side's first goal at San Mames.
Casillas was furious after the controversial goal, which saw Gabriel Heinze score against his own team, as Wesley Sneijder was on the ground injured.
"Yeste pushed me very hard. Even though he did not hit me in the face, it was still a red card," the EURO 2008 champions said after the game.
"I know I approached him before it, but without malice, but he suddenly pushed me and it changed the game.
"I had put the ball out previously when one of their players was down, but they did not do it for Sneijder."
Real extended their unbeaten Primera Liga run to 12 games with the win that saw Dutchman Klaas-Jan Huntelaar score twice in the process.