The Big Yin spoke of the power of forgiveness in an interview with Kirsty Wark on The Review Show on BBC Two on Friday night.
He said sexual abuse was a "very odd affair" and that for a long time he did not want to talk about it.
The 70-year-old, whose latest film role is in Dustin Hoffman's directorial debut, Quartet, was abused by his father between the ages of 10 and 15.
He told Wark: "I just didn't want to talk about it. It was mine and I kind of liked it being mine. I thought it made me very colourful, but it was up to me to make of it what I wanted to, and I always thought it made me kind of special.
"I loved him, and I kept loving him, and I love him today. And you know, forgiveness is a great thing –the power of forgiveness is immense and you can forgive dead people.
"It is a very odd affair, sexual abuse. Mine is very, very typical –you don't tell anybody about it.
"Everybody wonders why people who are abused don't rush off to the police or the authorities or an aunt or an uncle and tell them. But it just doesn't happen because you feel you've taken part in it - So there is a deep guilt and shame involved and so you don't tell people."
Connolly first revealed the abuse in a biography written by his wife, therapist Pamela Stephenson, in 2001 – 12 years after his alcoholic father, William, died.
In the book, he described how his mother left the family when he was three, leaving him to be brought up by his father and two aunts.
He said he and his father – who appeared alongside his son in a BBC documentary in 1978 – regularly shared a bed together in their flat in the Partick area of Glasgow.
Connolly also described how his Aunt Mona had regularly humiliated him by rubbing his underpants in his face and leaving notes saying "thief" in the biscuit jar.
He spoke of how she had found a copy of the "dirty" poem, Eskimo Nell, in his possession and had humiliated him with it for years.
Connolly added: "It was a schoolboy thing, it was a very dirty piece and she found it and humiliated me with it for years and years and years and threatened to take it to school.
"She was always going to tell my dad and he was going to beat me limbless. But it was every day, was the thing. Every single day."
Connolly, who was given the Freedom of Glasgow in 2010 and is considered one of the most famous Scots, also answered questions about his identity.
He said: "I think of myself as a Glaswegian before I think of myself as a Scot, although I am very proud to be a Scot. I find it quite difficult to think exactly who I am or where I live. I'm not sure where I live.
"I have the New York place, and Scotland, a wee place in Gozo, Malta, and I like them all very much, but I'm not sure which one is where I live or where my address is."