Harry said: “It was probably one of the biggest mistakes of my life. I felt so ashamed afterwards. All I wanted to do was make it right.”
He added: “I could’ve just ignored it and probably made the same mistakes over and over again in my life. But I learned from that.”
Harry, who was aged 20 at the time, was pictured holding a drink and cigarette while wearing the costume.
At the time, Clarence House issued a response saying Harry had apologised for any offence or embarrassment caused.
But just four years later, in 2009, Harry made headlines again on race when he was caught on film calling a former Army colleague “our little P*** friend”.
His comments today came as he discussed unconscious bias within the royal family. The programme made reference to Princess Michael of Kent wearing a Blackamoor-style brooch to an event the Duchess of Sussex attended in 2017.
Harry said: “In this family, sometimes you are part of the problem rather than part of the solution. There is a huge level of unconscious bias.
“The thing with unconscious bias, it is actually no one’s fault. But once it has been pointed out, or identified within yourself you then need to make it right.
“It is education. It is awareness. It is a constant work in progress for everybody, including me.”