"Rude and racist are not the same," said Meghan Markle while discussing online attacks on herself compared to how tabloids covered Kate Middleton

Meghan Markle is speaking out about how the press treatment sister-in-law Kate Middleton experienced upon her entry into the royal family did not compare to what the former Suits star has faced.

On Monday's episode of CBS This Morning, Oprah Winfrey offered more insight and new clips from her sit-down interview with Meghan and Prince Harry, which aired Sunday on CBS. In one new segment shared Monday morning, the pair discussed the "toxic" environment of the British tabloids surrounding the royal family.

"This was different," Meghan, 39, said of how the press covered her. Oprah then asked, "Different because of the race?" to which Meghan responded, "And because of social media."

For more on Prince Harry and Meghan Markle's interview with Oprah, listen below to the episode of PEOPLE Every Day.

"It was like the Wild, Wild West. It spread like wildfire. Plus, my being American — it translated in a different way across the pond. So you had a noise level that was very different," she added. "But if they can't see that it's different ..."

"So you felt bullied on an international level?" asked Oprah.

"Look," said Meghan, "I think the volume of what was coming in and the interest was greater because of social media, because of the fact that I was not just British, and that, unfortunately, if members of his family say, 'Well, this is what has happened to all of us.' If they can compare the experience of what I went through with similar of what has been shared with us ...."

Can't get enough of PEOPLE's Royals coverage? Sign up for our free Royals newsletter to get the latest updates on Kate Middleton, Meghan Markle and more!

She continued: "Kate was called 'Waity Katie,' waiting to marry William. While I imagine that was really hard — and I do, I can't picture what that felt like — this is not the same," said Meghan, while explaining how negative coverage of Kate, 39, did not equate to what she faced. "And if a member of his family will comfortably say, 'We've all had to deal with some things that are rude,' rude and racist are not the same."

"And equally, you've also had a press team that goes on the record to defend you, especially when they know something's not true. And that didn't happen for us," she said.

Also during the interview, Meghan spoke about people trying to create a narrative that pits her against her sister-in-law, whom she called a "good person." She said, "If you love me, you don't have to hate her. And if you love her, you don't have to hate me."

First Annual Royal Foundation Forum
Meghan Markle and Kate Middleton in Feb. 2018
| Credit: Chris Jackson - WPA Pool/Getty Images

Shortly after Harry, 36, and Meghan's relationship became public in 2016, the prince confirmed their romance with a rare public statement slamming the racist and sexist comments being directed at her at the time.

"His girlfriend, Meghan Markle, has been subject to a wave of abuse and harassment," the statement read at the time. "Some of this has been very public — the smear on the front page of a national newspaper, the racial undertones of comment pieces; and the outright sexism and racism of social media trolls and web article comments."

The statement continued: "It is not right that a few months into a relationship with him that Ms. Markle should be subjected to such a storm. He knows commentators will say this is 'the price she has to pay' and that 'this is all part of the game.' He strongly disagrees. This is not a game — it is her life and his."

Meghan and Harry married in May 2018, and share son Archie, 22 months. The couple is currently expecting their second child, a daughter.

During the Sunday interview, Meghan also revealed that while she was pregnant with Archie there were "concerns and conversations about how dark his skin might be when he's born."

Harry and Meghan did not identify who made the remarks, though Oprah said during an appearance on CBS This Morning Monday that it was not Harry's grandparents, Queen Elizabeth and Prince Philip.