According to a Reuters report he apologised:
The Muslim Council of Britain (MCB), an umbrella group for British Muslim organisations, said Harry's language had been unacceptable and had harmed the image of the army, which has been trying to recruit more widely from minorities.
But MCB spokesman Inayat Bunglawala said Harry had done the right thing by apologising. "It's now time to move on," he said.
And from the bbc:
I didn't know [it] was an insult," he said. "When I was little, I'd heard lots of people use that word and had never seen anyone scowl or seem upset, and I'd never considered those people [using the word] to be racists," he said.
"I was 21, I'd grown up isolated from the real world and surrounded by privileges, and I believed that word was like saying 'Yankee'. Innocuous."
Harry said his father's office released a statement on his behalf, and that although he wanted to put out his own statement, staff advised against it.
^^
"In any case, Ahmed was the person who mattered," he wrote. "I contacted him directly and asked for his forgiveness. He said he knew I wasn't a racist, that it was alright. But it wasn't alright. And his forgiveness, his natural deference, only made me feel worse."
I don’t think he was passing the buck when explaining how he grew up, I think he was explaining how he grew up in his book about his life up until 2022.
BBC article
He apologised: I’m yet to hear any other royal speak to their racism, yet Harry grew up in this family and family is where we learn first. We learn it as children from the adults around us. He didn’t absorb it from nothing. Diana very well told him off, but where did he first learn this behaviour? Kids don’t think up racism on their own. It’s not innate, it’s learned. My impression of Harry now is that he’s still learning to do better and be better.