He says, "I think part of her sickness is what made her live her life and really cherish the moments she had and cherish the people she was with. She did when she was with us, cherish those moments, and they made us all love her.
"She left an indelible impression on me. You don't really need much time to work or meet somebody and know that they're really alive... and when I heard that (she was sick) I just thought there's that moment when you go, 'Like, maybe that might be why she was so extraordinary.' And it makes me want to encourage people to wake up and live it like Jill did."
And the Brokeback Mountain star credited Clayburgh with helping his own mother through her divorce from the actor's father.
He explains the actress' portrayal of a divorcee in An Unmarried Woman gave his mum confidence when her marriage came to an end: "It helped her through that time in a way that no other movie or anybody else had."
Clayburgh, 66, died after losing a 21-year battle with chronic lymphocytic leukemia.