The Irish Catholic primate has admitted he was part of a culture which put avoiding scandal above bringing clerical child abusers to justice.
It emerged last month that Cardinal Sean Brady was present when children signed vows of silence over allegations against a paedophile priest in 1975.
In his Easter homily, Cardinal Brady said the Pope referred to a "misplaced" concern for the Church's reputation.
"There is now no hiding place for abusers in the church," he said.
Cardinal Brady, who is head of the Catholic Church in Ireland, has previously apologised for his role in mishandling the case of serial child abuser, Father Brendan Smyth, who was eventually convicted of dozens of offences against children over a 40-year period.
Speaking on Easter Sunday, Cardinal Brady said the desire to avoid scandal had meant proper procedures were not followed and "until recent times" abusers were not brought before the courts.
"I realise that, however unintentionally, however unknowingly, I too allowed myself to be influenced by that culture in our church, and our society," he said.
"I pledge to you that, from now on, my overriding concern will always be the safety and protection of everyone in the church - but especially children and all those who are vulnerable."
Meanwhile, the Bishop of Down and Connor has called on Catholics to show support for the church by attending Mass.
Bishop Noel Treanor was responding to comments made by the Archbishop of Canterbury about paedophile priests.
Dr Rowan Williams said the Catholic Church in Ireland had "lost all credibility". He has since said he regrets the impact of his comments.
Bishop Noel Treanor said the remarks were unfortunate and asked Mass-goers not to turn their backs on the church.
"What I would say to them to encourage them to come along is to recognise that in every one of us there is the capacity for evil and for failure, but none of us can throw the stone," Bishop Treanor said.
"By becoming part of the church they can, through their comments and their efforts, improve the quality of any Christian church and also the credibility of its witness."
The Archbishop of Canterbury's claim that the Irish Catholic church had lost all credibility because of its handling of child abuse by priests was criticised by both Catholic and Anglican clergy.
The Catholic Archbishop of Dublin, Diarmuid Martin, said he was "stunned".
Dr Rowan Williams later telephoned Archbishop Martin to insist he meant no offence to the Irish Catholic Church.
BBC religious affairs correspondent Robert Pigott said Dr Williams' words represented unusually damning criticism from the leader of another Church.
He made his comments about the scandal in an interview to be broadcast on BBC Radio 4's Start the Week programme.
Dr Williams said: "I was speaking to an Irish friend recently who was saying that it's quite difficult in some parts of Ireland to go down the street wearing a clerical collar now.
"And an institution so deeply bound into the life of a society, suddenly becoming, suddenly losing all credibility - that's not just a problem for the church, it is a problem for everybody in Ireland."