Stone starred in Verhoeven's 1992 film Basic Instinct and Scorsese's 1995 movie Casino. On The Late Show, Stone said Verhoeven and Scorsese gave her the best advice of her acting career.
"Paul Verhoeven told me that my talent was like an angel that would fly through me and that I needed to get out of its way," Stone said. "And I think that that was very good advice."
Stone was nominated for an Academy Award for Best Actress for her role as Ginger McKenna in Casino.
"And Marty Scorsese very much was also -- they were willing to tell me about their own lives, and they were willing to create a space with me where they would lean in and sometimes put their forehead on my forehead, both of them, and just hold the space around me so that I would have a space to be," she said.
Stone said film sets are typically "a very chaotic" and frenetic environment.
"So a director that will literally put their mind to your mind and look at you and talk to you and really get in there with you, those are the most helpful to me," she said.
Stone said great directors "protect" their actors and create "a small, protected space" for actors to draw on their emotions while filming.
"You're bringing emotion. You're bringing this out of yourself. A lot of people, honestly, they don't really get what that takes," the actress said.
"Many people are trying to get so much else from you while you do that, that you almost feel like you're going to snap," she added. "And you're criticized if you do snap."
Stone previously praised Scorsese while attending the actor's AFI Lifetime Achievement Award ceremony in 2010, calling him one of "America's finest filmmakers." She also appeared in Scorsese's 2019 film Rolling Thunder Revue: A Bob Dylan Story.
Stone most recently appeared in the Netflix series Ratched. She will release a memoir, The Beauty of Living Twice, on March 30.