"I never thought that this would be easy, but I thought that it would be fair," Meghan Markle said about her treatment by the media in a new documentary which debuted Sunday on Britain's ITV.

The American-born Markle, now the Duchess of Sussex, said out loud what many observers have guessed: she is finding the near-constant critical scrutiny as a royal very hard.

Meghan Markle, the Duchess of Sussex, interviewed in the ITV documentary, "Harry & Meghan: An African Journey." ITV

In the film "Harry & Meghan: An African Journey," she and her husband, Prince Harry, opened up about their struggles with the media's intense scrutiny of their personal lives. "Any woman when they're, especially when they're pregnant, you're really vulnerable," she said. "And so that was made really challenging. And then when you have a newborn, it's a lot."

The royals spoke about their complicated relationship with the press to ITV journalist Tom Bradby, for the documentary which followed them on their recent 10-day Southern Africa trip, which they took to bring attention to various charities. And as correspondent Elizabeth Palmer reports, their complicated relationship with the press has proved extremely stressful.

On camera, Meghan speaks about her bruising clashes with the British tabloid press.

"I've really tried to adopt this British sensibility of a stiff upper lip," she said.

"Has its advantages, I guess?" asked Bradby.

"I tried to … I tried, but I think what that does internally is probably really damaging," she said.

On the last day of that tour, Meghan and Harry sued one of those tabloids for what they said was a smear campaign.

The paper, The Mail on Sunday, had printed a very personal, and painful, letter that Meghan had written to her father. Prince Harry, who grew up watching his mother, Princess Diana, being hounded by the tabloids, was furious.

"Every single time I see a camera, every single time I hear a click, every single time I see a flash, it takes me straight back," Harry said.

Since their wedding, Harry and Meghan have tried to keep their private lives private, but that in itself has drawn criticism. Asked whether he and his brother, Prince William, are on the outs, Harry dodged the question:

"I love him dearly, and the majority of stuff is created out of nothing," he said. "But as brothers, you have good days, you have bad days."

Royal correspondent Roya Nikkhah told "CBS This Morning": "They are breaking the mold within the institution to a certain degree. Everything they do is being held to account, almost more closely and with more scrutiny than other members of the royal family at the moment."