CBS This Morning aired the clip Monday -- new footage from the couple's interview that aired on CBS Sunday night.
"Did you leave the country because of racism?" Winfrey asked the couple.
"It was a large part of it," Harry said, recalling someone at a fundraiser telling him the U.K. was bigoted.
"I stopped and I said, 'The U.K. isn't bigoted; the U.K. press is bigoted, specifically the tabloids. Is that what you mean?' He goes, 'No, the U.K. is bigoted.' I said, 'I completely disagree.' But unfortunately if the source of information is inherently corrupt or racist or bias, then that filters out to the rest of society," Harry said.
CBS This Morning also showed footage of Harry explaining how he and Markle were invited to spend time with his grandmother, Queen Elizabeth II, after they announced in January 2020 that they were stepping back as senior members of the royal family.
The plans were then abruptly changed, Harry said, with the queen suddenly becoming busy all week.
"Doesn't the queen get to do what the queen wants to do?" Winfrey asked.
"No. When you're the head of the firm, there are people around you that give you advice. And what has also made me really sad is that some of that advice has been really bad," Harry said.
Winfrey confirmed on CBS This Morning that Harry did not tell her who had conversations with him about the color of his son Archie's skin. Winfrey said she knows it wasn't his grandmother or his grandfather, Prince Philip.
In another clip shown on CBS This Morning, Winfrey asked whether any members of the royal family apologized for making Harry and Markle feel like they needed to get away.
"I think he's had to make peace with it," Harry said.
Markle, in extra footage with Winfrey, discussed how the tabloids tracked down her father, Thomas Markle.
Meghan Markle said she offered her father help in dealing with the tabloids but that he refused. Her father ultimately started cooperating with the tabloid press on a story.
"'I just need you to tell me. And if you tell me the truth, we can help.' And he wasn't able to do that,'" she recalled about a conversation she had with her father.
Meghan Markle also said she isn't close with her half-sister, Samantha Markle, who Winfrey said is set to release a tell-all book. Meghan Markle said she grew up as an only child and last saw Samantha 18 to 19 years ago.
"She changed her last name back to Markle...only when I started dating Harry. So I think that says enough," Meghan Markle said.
The couple's interview with Winfrey ran in a two-hour special on Sunday, addressing a host of issues surrounding their departure from Britain. Meghan Markle said she sought help for suicidal thoughts while pregnant and living with the royal family, but was rebuffed in seeking help.
The couple, who now live in Montecito, Calif., also revealed they are expecting baby girl this summer.