The former tennis player turned presenter had been hosting Question of Sport – the world's longest running TV sports quiz show – for 24 years until 2020, when the broadcaster decided to rebrand the show with a new host.
Barker told another BBC show, BBC Breakfast , that her employer had wanted her to say she was stepping down by choice, rather than being replaced.
She said: "They [BBC] wanted to refresh the programme and that's absolutely fine.
"So we knew it was going to happen and it was just the way in which it happened and the way it was handled, and the way I think the BBC wanted me to say that I was walking away from it.
"And yet, I'd never walk away from a job I loved. I didn't mind being replaced. Absolutely fine. That happens. But it was just the way it was handled.
"I think if we look back on it we could have handled it better. I think the BBC could have handled it better."
In her recent memoir, Barker also said she refused to put her name to any statement that claimed she was stepping down by choice, and that the experience had left her "slightly damaged."
"Did they actually expect me to sack myself?" she wrote.
Barker told BBC Breakfast : "It's just such a shame because I loved it.
"And I don't look back on it badly just because of a couple of bad days and then some negative publicity, which I think affected quite a lot of people."
Barker, the French Open champion of 1976, had also presented the broadcaster's Wimbledon coverage for decades until she announced her retirement from the job in July this year.
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