Speaking to the London Evening Standard to mark the start of Black History Month, the couple spoke of their hope for equality, and Harry, 36, of how he had become more aware of issues surrounding race after his marriage to Meghan, 39.
He said: "I wasn't aware of so many of the issues and so many of the problems within the UK and also globally as well. I thought I did but I didn't.
The prince added: "You know, when you go into a shop with your children and you only see white dolls, do you even think: 'That's weird, there is not a black doll there?'
"And I use that as just one example of where we as white people don't always have the awareness of what it must be like for someone else of a different coloured skin, of a black skin, to be in the same situation as we are, where the world that we know has been created by white people for white people."
The couple said that while there has been "unquestionable progress" to tackle racism, they added "in many ways sufficient progress has not been achieved" in the three decades that Black History Month has been observed.
Harry and Meghan stepped down as senior royals earlier this year, and now live in Santa Barbara, California.
During the video call from the States, they revealed their list of BHM Next Trailblazers, recognised for challenging prejudice and their positive contribution to British society.
The influential black Britons included England rugby player Maro Itoje, Vogue editor Edward Enninful, Olympic boxing champion Nicola Adams and Booker prize-winning author Bernardine Evaristo.
Writing in an article for the paper, the Duke and Duchess said: "For as long as structural racism exists, there will be generations of young people of colour who do not start their lives with the same equality of opportunity as their white peers.
"And for as long as that continues, untapped potential will never get to be realised.
"If you are white and British, the world you see often looks just like you - on TV, in media, in the role models celebrated across our nation.
"That is not a criticism; it's reality.
"Many recognise this, but others are not aware of the effect this has on our own perspective, our own bias, but also the effect it has on young people of colour.
"For people of colour and specifically for young black Britons, the importance of representation in all parts of society, of seeing role models that share the same colour skin as them, and seeing and reading stories of success and of hope from those who look like them, is absolutely vital in opening doors of opportunity."
Meghan also spoke about how Baroness Lawrence - mother of murdered Stephen Lawrence - inspired her.
She said: "Everything she has done in memory of her son is creating legacy across the UK in what it means to really push for the change that is necessary."
She also spoke about how the raft of complaints aimed at the Diversity performance supporting the Black Lives Matter movement, showed that "this conversation needs to continue".