Bishop Kirby, 73, said that 20 years ago he "hadn’t a clue" about how paedophiles operated, and thought paedophilia was "a friendship that crossed a boundary line".
Dr Kirby, who has been the bishop of Clonfert since 1988, said he had felt moving the priests to new parishes might solve the problem, but denied it was Church policy at the time.
"I think that is unfair presumption on the part of people. I literally thought, and you can put it down as gross innocence and naivety, that if I separated the priest and the youngster... I would have solved the problem. I was not aware that youngster was part of a group and that there were people before him and after him."
Nine allegations were made against two priests in the early 1990s. One was convicted and served a jail term but the other was not prosecuted as his victims declined to make statements to the gardaí. The third priest was dead for four decades when allegations were made against him.
Bishop Kirby said he reported the allegations to the Western Health Board and presumed it would report them to "civil authorities", including gardaí.
The bishop said that if he reacted now as he did when the cases occurred, he "would be gone in the morning".
"It did not occur to me [to resign]. Times were very different. It was 1990 in the first case and 1994 was the second. There were no guidelines available at that time.
"Clearly, if it was now, I would have no question, I would not consider resigning. I would be gone in the morning."
Bishop Kirby said the priests at the centre at the allegations were not monitored when they were moved to other parishes.
"It would be dishonest of me to say that there was monitoring. There was wishful thinking.
"I now know that the whole issue of child sexual abuse is compulsive and addictive and that my response was grossly inadequate."
Bishop Kirby said he wished to apologise to the victims and their families.
"I wish to apologise for my own previous lack of understanding of the sinister and recidivist nature of the child abuser, and the life-long damage that this destructive behaviour has on victims. Most of all... I profoundly regret and apologise for moving the priests concerned to different parishes thereby placing others at serious risk."
Bishop Kirby said he was now confident the necessary safety measures were in place in his diocese.
"There is a full range of policies based on the Safeguarding Children process that has been established in Maynooth. We have our own diocesan committee, the full policy is sent to priests and to the local safeguarding representatives."