Harry said that some members of the family felt negative treatment in the media was "a rite of passage" - but he claimed, "The difference is the race element."
The first three episodes of the six-part bombshell series titled "Harry & Meghan" were released on Thursday. The couple talk about life in the Royal Family, press intrusion and racism.
At the start of episode one, a message says that members of the Royal Family declined to comment on the series. But both Buckingham Palace and Kensington Palace say that neither they, nor any other members of the Royal Family, were approached for comment.
The episodes released on Thursday - which include sit-down interviews with the couple and their friends, as well as a video diary - cover a range of topics, including the couple's difficult relationship with the tabloid press, and the Royal Family's response to racist news articles written about Meghan.
Source: Netflix & BBC