Bishop Murray was previously an auxiliary bishop in Dublin and the Commission of Investigation heavily criticised how he dealt with complaints.
Fr McCafferty, currently based in Rathmines parish, said that Dermot O'Mahony, an assistant bishop in Dublin who did not tell his Archbishop about complaints, was now ill.
"Bishop O'Mahony is an ill man and an ailing man," he added.
Fr McCafferty, a native of Belfast, was abused by a babysitter and a male neighbour when he was a child. It was always his ambition to enter the priesthood.
"I fell prey to this priest in our diocese at home who kind of adopted me," he said.
"At first, he was fine and he was good and friendly and all that. And then it turned sinister and it became abusive and he used force.
"People say to me, 'How could you go on after what happened?' But my faith in God was strong enough. If I didn't believe in God, I think I would have taken my own life."
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