The former actress, who lives in California with Prince Harry and their children Prince Archie, six, and Princess Lilibet, four, shared the detail during the second season of her Netflix series With Love, Meghan.
"Some of the words that they still say with a British accent. "So they'll say, 'Ze-bra,' and what else do they say? They have these little moments where it comes out," she said on the program.
"They have very American accents, but they say words that are just like him, and I think it's adorable. Zebra is a good one."
Meghan also spoke about differences in her own pronunciation compared to Harry.
"My husband always laughs when I say 'herbs' – he's like, 'Herbs.' He's like, 'You're so American — 'Erbs, 'erbs.'"
Meghan and Harry stepped back from royal duties in 2020 and relocated to California, eventually settling in the Santa Barbara enclave of Montecito, where Lilibet was born in 2021.
The eight-episode second season of With Love, Meghan features appearances from Chrissy Teigen, Tan France, Jay Shetty, Radhi Devlukia, José Andrés, Clare Smyth, David Chan and Samin Nosrat, alongside Meghan's friends Jamie Kern Lima, Heather Dorak and Daniel Martin.
Earlier this month, Harry and Meghan announced their creative partnership with Netflix had been extended in a multi-year first-look deal for film and television.