Ethan Hawke Reveals the Advice Denzel Washington Gave Him After Oscar Loss for Training Day

Awards don't define Denzel Washington — just ask Ethan Hawke.

In the most recent episode of Who's Talking to Chris Wallace?, host Chris Wallace asked Hawke, 53, whether it was true that his Training Day costar Washington whispered into his ear at the 2002 Academy Awards, "It's better that you didn't win. Losing was better."

While Hawke didn't confirm or deny that those were the exact words from his costar — who won Best Actor that year for his role in Training Day — Hawke said of Washington, 69, "You don't want an award to improve your status — you want to improve the award's status. That's the way he thinks."

"The Academy Award has more power [now] 'cause Denzel has a couple. It didn't elevate who he was," Hawke explained.

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Asked by Wallace, 76, whether he would have liked to win the Best Supporting Actor award, which he lost to Jim Broadbent for his role in the biographical drama Iris, Hawke said he felt like a winner just to be surrounded by some of the greats.

"I was at the Oscars sitting next to Denzel Washington and nominated against Ian McKellen. I had already won. It was impossible for me not to see it any other way," he replied.

Wallace also asked the actor about having compared Washington to Babe Ruth, which Hawke explained, "I think when all is said and done, [Denzel is] the greatest actor of our generation."

"I imagine, if you loved baseball, it would be interesting to see how Babe Ruth tied his shoes. You know? How he thought about various pitchers. The whole process," he added. "But what creates that is a tremendous amount of energy and thought, what creates those moments."

"And once you see somebody working that way, there's all these other rooms that you can go into in the profession," Hawke said.

Hawke is gearing up to release his movie Wildcat, which he directed and co-wrote and is in theaters Friday, May 3. It stars Maya Hawke, the actor's daughter with ex-wife Uma Thurman.

Maya, 25, plays writer Flannery O'Connor in the 1940s and 1950s, when she was in her 20s and struggling to get her first novel, Wise Blood, published. O'Connor, who died in 1964 at age 39, was also diagnosed with lupus during this time in her life.

"Anybody that knows Maya knows that she's a force,” Hawke said of his daughter when PEOPLE exclusively premiered the trailer for Wildcat on March 13.

"She always has been," he added. "She writes and performs her own music and she loves acting and she loves painting and she's kind of an artistic animal.”

Who's Talking to Chris Wallace? is streaming on Max, with new episodes every Friday.