It follows reports that the documentary had upset the royal family who wanted the opportunity to view the film before it aired, plus respond to claims made.
In a statement at the end of the first episode, Buckingham Palace doubled down on the mood presented from unnamed sources, The Daily Mail reports.
A statement at the end of the doco reads: "A free, responsible and open press is vital to a healthy democracy. However, too often overblown and unfounded claims from unnamed sources are presented as facts and it is disappointing when anyone, including the BBC, gives them credibility."
The first episode, which aired in the UK on Tuesday morning NZ time, covers William and Harry's relationship from 2012 up until 2018 when the Duke and Duchess of Sussex married.
It introduces the beginning of a reported "rift" between the Sussexes and the Cambridges.
The next episode will focus on the downfall of relations between the two royal couples and will feature claims the Royal family leaked the news Harry and Meghan leaving in an effort to undermine negotiations, the Telegraph reports.
It will also include claims members of the royal household fed information to the press about the so-called rift.
An unnamed source told the Daily Mail ahead of the documentary airing:
"There is upset about it. The households are all united in thinking this is not fair. No one at the Palace has seen it."
Allegations of bullying were made against Markle in October 2018 by communication secretary Jason Knauf, who worked for the Sussexes. The complaint alleges that Markle drove two personal assistants out and was undermining the confidence of another staffer.
Buckingham Palace launched an internal investigation into the claims.
