"It is not about pointing the finger, it is not about blame. I will be the first person to say, again, this is about learning," Harry told the paper.
"And about how we can make it better. I think it is a really exciting time in British culture and British history, and in world culture," added Harry, who is Queen Elizabeth's grandson and sixth-in-line to the throne.
"A beautiful thing"
The interview, carried out by video from their new home, coincides with the start of Black History Month in Britain which celebrates the contribution of Black people to the nation.
However, the Sussexes have faced accusations in the British media that they are not respecting the tradition that the royal family does not comment on political matters.
Last week, they encouraged Americans to vote in the November presidential election, with Prince Harry saying it was "vital that we reject hate speech, misinformation and online negativity".
Critics said his comments could be understood as a call to vote against US President Donald Trump. Buckingham Palace said the remarks represented Harry's personal views.
The paper said Harry had accepted in the interview that their views "may seem controversial".