Lord George Carey launched the second instalment of his memoirs, The Truth Will Set You Free, at the Christian Resources Exhibition on Thursday.
Speaking at the launch of the book, published by Barnabas Fund, the former Archbishop of Canterbury said it contained two "very, very painful" chapters on abuse looking at the Peter Ball case and accusations against his son Mark Carey.
He said the claims against Mark were "total nonsense" and that although the police later cleared him, the experience had been one of "humiliation".
Concerning Peter Ball, who was jailed for abuse in 2015 before dying in 2019, Lord Carey said he had made "profound mistakes".
"I regret those very deeply. That was 25 years ago and we have learnt so much since," he said.
His comments at the launch touched on a wide range of subjects, among them his "change of heart" on assisted suicide.
He said a "key moment" in his thinking on the subject came with the case of Tony Nicklinson, a man with locked-in syndrome who lost his right to die case at the High Court in 2012. He died a week later after refusing food.
Lord Carey said, "I came to the conclusion I had to give my support on compassionate grounds: what would Jesus do if he was alive today? I'm pretty sure he would support any effort to allow people to die without pain."
But he admitted his views were in "total opposition" to the Church of England on the subject.
He also commented on George Bell, who he said had been "vilified" by the Church of England despite being "one of the great heroes of the War years".
"The accusations against him, the cloud that still hangs over him, is completely wrong. His record is straight, he did nothing wrong," he said.