Washington explained the chain of events that led to his firing during an appearance on CNN's "Larry King Live" Monday night, his first televised interview since leaving the show.
Washington, who was accused of referring to actor T.R. Knight using an anti-gay slur during the heated argument with Dempsey, said that in reality he was referring to himself.
The argument, which he said stemmed from his frustration with Dempsey supposedly being late to the set, heated up to the point where it almost got physical.
"(Dempsey) became unhinged, face to face, spittle in my face. I'm asking him 'why are you sceaming at me?' He became irate. By that time I pushed him out of my face and I began to say 'there's no way you're going to treat me like a 'b word,' a 'p word,' or a 'f word' in front of this crew."
Washington thinks the outcome of the situation would have been different if he had used the "n-word" instead.
"I wish I had said 'You're not going to treat me like an 'n-word' because that's how I felt," he said.
The story about the argument was leaked to the National Enquirer and was picked up by blogs and other tabloids. Shortly afterwards, T.R. Knight revealed that he is gay and told Ellen Degeneres on her show that Washington was referring to him when he used the anti-gay slur.
Things seemed to die down as the weeks went by, but Washington opened up fresh wounds in January during cast interviews in the press room backstage at the Golden Globes. After a tabloid reporter repeatedly questioned cast members about the October argument, Washington blurted out, "I never called T.R. Knight a 'faggot.'"
"I unbelieveably regret that," he said about the comment. "If I could take that moment back. (The story) wasn't true and unfortunately I did what you don't do, and that's go to IMDB or blogs and read what they're saying about you. I felt that my integrity was being challenged."
The Golden Globes appearance caused an uproar, and after protests from GLAAD and other gay watchdog groups, Washington was formally reprimanded by ABC and he agreed to do a public service announcement and get counseling.
Producers did not renew Washington's option on his contract with "Grey's Anatomy." The actor told King that he had tried to quit twice but his resignation was not accepted.
King asked Washington why he wanted to come on his show to talk about the controversy.
"My publicist Howard Bragman was tipped off that there were some leaks," Washington said. "That (during) my entire tenure there had been problematic behavior which had been exhibited and that I had other transgressions. That's the reason I'm here." Washington did not elaborate further on the supposed leaks.
According to King, ABC and Dempsey's rep both declined to comment about Washington's interview and a representative for TR Knight said "no comment."
Washington did say he learned something valuable from his experience.
"Focus on your acting. Don't worry about production issues, and in times of great stress and duress just keep your mouth shut," he said.