Robbins won his first Oscar for his performance as a man who was a victim of child abuse. He was nominated once for Best Director for "Dead Man Walking."
In his acceptance speech, Robbins urged victims to report their abuse, rather than stay silent.
"If you are out there and a person who has had that tragedy befall you, there is no shame or weakness to seeking counseling," he said. "It is the strongest thing you can do to stop the cycle of violence."
Robbins credited his "Mystic River" director, Clint Eastwood, with guiding his performance.
"Clint Eastwood, you're great," said Robbins. "You're a great director and you're making my mantel very crowded."