Sue Parker says she is "sad" her role in the sport is over and the BBC can do "better".
The 66-year-old broadcaster started hosting the sports competition show in 1997 and left in 2021.
Appearing on BBC Breakfast , he suggested the company ask him to say he resigned voluntarily rather than being replaced as part of a "reshuffle".
Read on. Sue Parker. He felt disrespectful to the BBC for kicking me out of the sport
"It's a shame because I have to say the BBC told us we were leaving," he said.
“They wanted to update the software and it's totally okay. Everyone has a right to it. We don't own the show.”
The former tennis player continued. "I've worked with the most amazing people for 24 years. So we knew it was going to happen and it happened that way and that's how it was handled and the BBC asked to say I refrained from doing it.
“However, I would never leave the job I love. I don't mind them being replaced. It's totally fine. It happens. But that's how it was handled."
"I think we regret the way it was handled. I think in hindsight we could have done better. I think the BBC could have handled it better."
Parker said it was a "huge embarrassment" because he "loved" the show.
"And I'm not turning it down just because of two bad days and then some negative publicity that I think affects some people," he said.
In September 2020, it was announced that Parker had left The Sports Question.
It was later confirmed that Buddy McGuinness would take on the role, with the show's captains Matt Dawson and Phil Tuffnell replaced by Sam Cake and Hugo Meunier.
Parker has since announced that he has also retired from covering Wimbledon tennis.
He later indicated that what happened to Question Of Sport led to his decision to leave Wimbledon before he was asked to leave.
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"The way it happened made me think of Wimbledon and want to come out on my own terms rather than get fired," Parker said, speaking on the Desert Island disc earlier this year.
Additional report to the Palestinian Authority.
Watch: Emotional Sue Parker receives a standing ovation during a celebration in Center Court