Ms Brown, who has written various books on the Royal Family, including several on Harry's mother, Princess Diana, believes Harry keeps "doubling down" on his mistakes.
When asked for her reaction by the BBC's Laura Kuenssberg, she said: "Well, what I thought was, after five years Harry is still at war with his original mistake.
"And every time he goes on the air, he makes another one – so it's like he is now trapped in this terrible cycle of doubling down on the original mistake."
Ms Brown, who is formally known as Lady Evans after the knighthood of her late husband, added: "I didn't hear two very crucial words in that entire sort of jeremiad about, you know, 'I'd like to reconcile, I'm sorry'.
"I mean, he never said, 'I'm sorry, I'm sorry I caused my family all of this pain'. That is really what they’re upset about, not the security."
The Duke declared he would write to the Home Secretary, Yvette Cooper, to ask her to urgently examine the matter and review the Ravec [Royal and VIP Executive Committee] process.
A government spokesperson explained how the committee was designed to be independent from political influence.
They added: "As part of long-standing arrangements, these decisions have been taken by Ravec, not the Home Secretary."
Ms Brown, who has also edited Tatler, Vanity Fair, and the New Yorker, added: "I think he thought he could just blow it off and in his reckless, sort of hot-headed Harry Hotspur way charged out of the Royal Family with all of these issues completely unresolved.
"There was no way that this court was going to go against the findings of the security, the police. They're not going to go against that and they're not going to go up against the police, against the Royal Family or the police."
Buckingham Palace issued a rare public statement following Harry's interview, saying: "All of these issues have been examined repeatedly and meticulously by the courts, with the same conclusion reached on each occasion."