In a clip of Oprah Winfrey's interview with the couple, Meghan had been asked how she felt about the palace hearing her "speak your truth today".
Meghan also said: "If that comes with risk of losing things, I mean... there is a lot that has been lost already."
Buckingham Palace is investigating claims the duchess bullied royal staff.
The allegations of bullying levelled at Meghan were published after the interview with Oprah was recorded.
The interview with Oprah, which will air in the US on Sunday and in the UK on Monday, is expected to detail Harry and Meghan's short period as working royals together before they stepped down for a life in the US.
In the 30-second teaser clip released by CBS, Oprah asks the duchess: "How do you feel about the palace hearing you speak your truth today?"
Meghan replies: "I don't know how they could expect that, after all of this time, we would still just be silent if there is an active role that The Firm is playing in perpetuating falsehoods about us."
The Duke and Duchess of Sussex quit their roles as senior working royals in March 2020, and now live in California.
A report in the Times newspaper on Wednesday claimed the duchess faced a complaint made in October 2018, while the duke and duchess were living at Kensington Palace after their marriage in May of that year.
A leaked email sent from a staff member, which was published by the newspaper, alleges that Meghan drove two personal assistants out of the household. The report claims she undermined the confidence of a third member of staff.
In a statement later, Buckingham Palace - which is responsible for the hiring of royal staff - said it was "clearly very concerned about allegations in the Times" and its HR team would look into the circumstances outlined in the article.
"The Royal Household has had a Dignity at Work policy in place for a number of years and does not and will not tolerate bullying or harassment in the workplace."
If anyone thought Prince Harry and Meghan were going to restrict their criticism to the British media, a sector they have made clear they loathe, they should think again. "The Firm" - aka the Royal Family and its staff - is clearly in their sights.
This isn't directly about the allegations of bullying levelled at Meghan, and also to a lesser degree Harry. They were published after the interview was recorded. But the couple see the allegations as an example of how some people in the palace brief against them.
We'll have to wait for the interview to find out exactly what "falsehoods" the couple believe have been put out by the palace. The bullying allegations - which are vigorously denied by the couple - are being investigated.
But it's clear that the gloves have come off, and that the ties of family have not restrained the couple as they seek to put their side of the story.
Past and present royal employees are to be invited to speak in confidence about their experiences of working for Meghan as part of the investigation.
The bullying allegations are denied by Meghan and Prince Harry.
A statement issued by Meghan's spokesman in response to the newspaper's story said: "The duchess is saddened by this latest attack on her character, particularly as someone who has been the target of bullying herself and is deeply committed to supporting those who have experienced pain and trauma.
"She is determined to continue her work building compassion around the world and will keep striving to set an example for doing what is right and doing what is good."
Author Anna Pasternak - who wrote a book on Princess Diana - said she thought "the whole issue stems to when Meghan first entered the Royal Family".
"I think she was naïve, she didn't really understand the monarchy or 'The Firm' as she rightly puts it, and the constricts of royal power. She was naive to think that she could modernise the monarchy, that she could have her voice and could do things her way," she told Radio 5 Live.
But Rachel C. Boyle, head of interdisciplinary studies at Leeds Beckett University, said the Oprah interview was "absolutely the right thing to do at this point".
"I feel like Meghan has not been given the opportunity to defend herself or to respond to any of the claims that have previously been made about her in the media, in a space that allows her to express herself."
Meghan and Prince Harry's TV interview with Oprah will be aired on CBS in the US on the evening of Sunday 7 March.
In the UK, the interview will be screened on ITV at 21:00 GMT on Monday 8 March.
CBS has said Meghan will be interviewed about "stepping into life as a royal, marriage, motherhood" and "how she is handling life under intense public pressure".
She will then be joined by Prince Harry, and the couple will speak about their move to the US last year and their future plans.
In an earlier clip released by CBS, the Duke of Sussex drew parallels between the treatment of his late mother, Diana, Princess of Wales, and Meghan.
Just hours before the interview is aired in the US, a special programme to celebrate Commonwealth Day will be broadcast on BBC One at 17:00 on Sunday 7 March.
It comes as Buckingham Palace announced that the Duke of Edinburgh has undergone a successful procedure for a pre-existing heart condition and will be remaining in hospital for a number of days.