Primate of All Ireland Archbishop Eamon Martin has said the Catholic Church understands why survivors of abuse find it difficult to trust the institution.
He said the proof of the Pope's visit will rest in whether or not there is decisive action from the church.
Speaking to RTÉ News, the Archbishop said the Pope had taken a lead in terms of abuse scandals.
He said he never before heard a Pope accept a personal responsibility for all the trauma and hurt, the crime and sins of abuse.
Archbishop Martin said the proof of the visit would be whether or not there was strong accountability in the church, the truth coming out, justice and healing for those that were hurt, and decisive action.
He said in Ireland they had already decided that all allegations of abuse were immediately reported to the civil authorities.
He said the church had realised that accountability in Ireland was to the people and through the law. He added it also ensured that if a priest admitted guilt or was found guilty they were removed from ministry.
Archbishop Martin said people were moved around and abuse was covered up in a false understanding that you were preserving the church from scandal.
He said that the religious authorities put the reputation of the church before victims and survivors.
Archbishop Martin said some survivors now recognised Ireland and a number of other countries had developed best practice in this, which must now be spread throughout the church globally.
During his visit, Pope Francis said he was not aware of the Magdalene Laundries and the mother and baby homes until he met survivors on Saturday evening.
The Archbishop said he personally did not speak to him on these matters, but the Pope was deeply moved by the accounts of survivors.
However, Archbishop of Dublin Diarmuid Martin told RTÉ Radio in April this year that he had told Pope Francis about the Tuam babies story and the Pontiff had become "visibly upset".
Asked would he call on those who hold records pertaining to adoption in this country to release them in light of the Pope's statement that mothers or adopted children who sought out their birth relatives did not commit sin, the Archbishop said they had already made that call but the law needed to change to facilitate this.
He said he advocated all records be turned over to the State so a proper search mechanism could be put in place for all those seeking their relatives.
However, he said the release of records was difficult because some people did want their records or identity given, but he believed it was surmountable and congregations he spoke to were open to this.
Speaking on the plane returning to Rome, the Pope acknowledged that Irish people had suffered a lot from the abuse scandals in the church.
However, he said: "But there is faith in Ireland. It's strong. And also the Irish people know how to distinguish.
"And I cite what today I heard from a prelate: the Irish people know how to distinguish well between the truth and half-truths. It is something that they have within. It’s true that it’s in a process of elaboration, of healing from these scandals.
"It’s true that positions are being opened that seem to distance themselves from any faith. But the Irish people have a deep-rooted faith."
Read more: Pope Francis in Ireland
Bishop of Limerick, Bishop Brendan Leahy, has said he believes Pope Francis acknowledged the "dark aspects" of the Catholic Church's history.
Speaking on RTÉ’s Today with Miriam, Bishop Leahy said his address at the Phoenix Park at the end of his visit marked a "whole new moment of hope in our history".
He said he was pleased with how the visit had gone and that every element surpassed expectations and said it marked a new beginning "for us".
In relation to the turnout of people over the weekend, he said that in the church they were not interested in numbers. He said that the important thing for the church was that it marked a new beginning of hope.
Bishop Leahy said he believed the visit could change things for the better for the church. He said it was not about saying everything had been resolved but that it was also about the importance of faith for some people.
Meanwhile, the editor of the Irish Catholic newspaper has said that following on from the Pope's language this weekend, there now needs to be action.
Speaking on RTÉ's Morning Ireland, Michael Kelly said it was necessary that accountability was part of the structures when dealing with clerical sex abuse.
He said he believed what was lacking in dealing with the matter of historical clerical sex abuse was how bishops who have been shown as having been negligent or who have covered up abuse are dealt with.
He said that action must follow all the words he used in his letter ahead of his arrival in Ireland, and in his speeches at the various Papal events.
Mr Kelly added that the issue was not going to go away by giving a few speeches.
