The actor told the SmartLess podcast hosts that at the time he thought, "I f***ing hate this business" adding, "I'm like, 'Bro, why are you such an a**hole?' I would never f***ing forget that. Go f*** yourself."
Cooper did not name the director.
It wasn't the first time the actor had faced criticism from his Hollywood peers.
In 2013 The Hangover actor was nominated in the Best Actor category at the Oscars alongside Daniel Day-Lewis, Hugh Jackman, Joaquin Phoenix and Denzel Washington, but one "hero actress" mocked his first-ever nomination at the awards show.
Cooper said, "This hero female actress, that I didn't know at all, comes up to me, she goes, 'I saw your movie. You deserve the nom,' "
"Then like 10, 20 minutes later — I'm not kidding — I pass her going to the bathroom and she mouths it: 'The nom.' I remember [thinking], 'What the f*** is this town?'"
"Can you imagine saying that to somebody? You've got to be f***ed up to do that."
Despite going on to get two more Academy Award nominations - for 2019's Joker and 2021's Nightmare Alley, both of which he co-produced and were up for Best Picture, Cooper admitted he felt "worthless" and "insecure" early on in his film career.
During the podcast episode, Cooper had a sweet moment with Arnett where they shared their emotional and mental health struggles as recovering addicts and said fatherhood has positively affected their relationships with themselves.
"Fatherhood is … everything changed," Cooper said. "Every single thing is absolutely shaded by or brought into glorious colours by the fact that I get to be a father to a wonderful human being."
The A Star Is Born actor shares five-year-old daughter Lea De Seine with his ex-girlfriend and model, Irina Shayk.