The prince spoke during a conversation about racism with Patrick Hutchinson, the Black activist who was photographed by Reuters carrying a white man to safety during a scuffle between anti-racism protesters and far-right opponents in London in June.
Harry told Hutchinson he saw him as a "guardian angel" protecting everyone at the demonstration. Both men said there was still work to be done to defeat discrimination of all kinds.
"Unconscious bias, from my understanding, having the upbringing and the education that I had, I had no idea what it was. I had no idea it existed," Harry said during the online conversation, recorded last week for a feature by the magazine GQ.
"And then, sad as it is to say, it took me many, many years to realise it, especially then living a day or a week in my wife's shoes," added the prince. Meghan's father is white and her mother is African American.
Harry and Meghan, the Duke and Duchess of Sussex, have spoken out several times on race issues since stepping down from their roles as working members of the royal family at the end of March and moving to California.
Hutchinson, 50, told Harry a friend who had been at a previous protest where a policewoman had been injured had gathered a group to see if they could help keep order.
"It was us protecting everybody and, as it turned out, somebody on the other side ... I would do it for anybody and I would do it time and time again," he said.
The prince asked him how he felt seeing the continuing opposition to anti-racism protests.
"It's frustrating," said the father-of-four. "It just makes you wonder why people find it so hard to understand what we're all striving for: the equality side of things."
