Meghan was interviewed by her friend on an episode of the U.S. daytime programme, which aired on Thursday (18Nov21), and she also took part in a sketch where she drank from a baby's bottle, claimed to have healing powers and impersonated a cat while out shopping.
However, Thomas Markle has insisted his estranged daughter shouldn't have gone on the show because it isn't appropriate for her position in the British royal family.
Thomas told the Sunday Mirror newspaper, "It's no way to behave. The whole thing was kind of embarrassing. It was certainly embarrassing for the Royal Family."
"It's embarrassing for her as well. I suspect it embarrassed everyone in the U.K., too."
"She's putting herself out there as a Duchess but I've never seen a Duchess behave this way, doing stupid stunts."
During her interview, Meghan recalled how she used to visit the Warner Bros. lot where the show is filmed for auditions as a struggling actress and made the audience laugh with a tale of how the car she drove at the time didn't even have opening doors.
However, the retired lighting director has insisted the anecdote wasn't true, sharing, "I'm disappointed she didn't mention me. I hooked her up with a director on the General Hospital TV show and that got her a couple of lines on one of the shows which got her a union card."
"It's really difficult to get a job without a card so that was crucial. I paid for the card too. I've been disappointed all this hasn't been acknowledged..."
"The Ford Explorer she had in her early 20s that she mentioned was a good running vehicle. I don't remember any time she had to crawl out of the back of it to get out, like she said."
"The doors worked fine on that vehicle until the day she got rid of it."
Meghan - who has Archie, two, and Lilibet, five months, with husband Prince Harry - also spoke about her children's book, "The Bench", but Thomas argued the story isn't interesting for kids.
He said, "That book is not for children. No child would read or understand that book. That is an adult's book, it's for her husband. No kid would be interested. The only thing interesting for a kid in that book is the picture of the dog on the cover."
Despite his comments, Thomas is still hopeful he can mend his differences with the former "Suits" star.
He said, "Sooner or later I do think as a family we are going to get together. It's sort of ridiculous we can't and it's all down to bad tempers. But for an old man I'm doing OK. I've got a bad heart, but I am doing all right."
"Before the wedding, she made speeches around the world, for the UN and so on, and said there 'should be more men like my dad'. So at that point we were in a good place, but it all went downhill when she met Harry."