Cardinal Seán Brady has admitted that with the benefit of hindsight, his actions in dealing with the hurt caused by clerical child abuse in the past were hopelessly inadequate.
It emerged this week that Cardinal Brady was present during meetings in 1975 when two young victims of paedophile priest Fr Brendan Smyth were asked to sign an oath of secrecy.
The Cardinal has been criticised for not reporting the allegations to gardaí.
Cardinal Brady said he was not the designated person responsible for contacting the relevant statutory authorities.
At St Patrick's Day mass this morning Dr Brady said he would be reflecting on whether people - who had made mistakes in responding to abuse victims - could have a part in shaping a new beginning for the Catholic Church.
'This week a painful episode from my own past has come before me. I have listened to reaction from people to my role in events 35 years ago.
'Looking back I am ashamed that I have not always upheld the values that I profess and believe in.'
The late Fr Smyth's religious order - the Norbertine Community - earlier apologised to Cardinal Brady and Smyth's victims for failing to remove the paedophile permanently from exercising his ministry as a priest.
In a statement, the Norbertine Community said that throughout Smyth's time as a priest, he was subject to its authority in all matters concerning his behaviour.
It added that it was clear the only effective means of dealing with a person of his propensity to sexually abuse children was through the rigour of criminal law.
The Norbertines say that on many occasions, over several decades, Fr Smyth availed of psychiatric and other forms of treatment but that none of these interventions had any effect.
Meanwhile, one of Brendan Smyth's victims has called on Cardinal Brady to hold an independent national inquiry into clerical child abuse.
Reacting to the Cardinal's homily today, 'Samantha' said the Cardinal must answer whether his inaction led to her being raped and abused.
Pope Benedict today said he hopes his imminent letter on the problem of child sexual abuse by priests will 'help repentance, healing and renewal'.
Speaking in English to pilgrims and tourists in St Peter's Square for his general audience, the Pope announced that he will sign his long-awaited pastoral letter dealing with paedophilia in Ireland on Friday. It is expected to be released on Friday or Saturday.