Ian Elliot, head of the Catholic Church's child abuse watchdog, called into question the competency of Bishop John Kirby over the remarks following his audit of the Diocese of Clonfert.
"Care needs to be taken when appointing a bishop that you do not appoint a bishop with these attitudes," Mr Elliot said. "These are basic competencies that everyone should have in authority. I'm not calling for anyone to resign but, for me, that's an absolute basic requirement."
Bishop Kirby, in charge of the diocese since 1989, made the ill-judged revelation on the back of apologies to survivors of two abusive priests he moved from one parish to another in 1990 and 1994. Although he signed off the transfers, he also notified gardai of the allegations.
Bishop Kirby claimed he did not understand paedophilia in an attempt to explain why he adopted the standard church response of the time to transfer clerical child abusers.
"I saw it as a friendship that crossed a boundary line. I have learnt sadly since that it was a very different experience," he told Galway Bay FM.
Clonfert was one of seven audits carried out by Mr Elliot's National Board for Safeguarding Children in the Catholic Church (NBSCCC).
Seven audits uncovered allegations against 146 clerics relating to 378 complaints of abuse.
Twelve convictions were secured, it stated.
Frances Fitzgerald, Children's Minister, said she has planned a series of meetings with Mr Elliot and also leaders of the congregations to discuss the audits.
"To think that such a culture and mindset continued to exist among sectors of our society until as recently as 12 months ago, is bitterly disappointing, it is deeply worrying and it is quite simply unacceptable," she said.
The NBSCCC has another 16 dioceses to audit and 162 congregations and missionary unions.