Bishop Philip Boyce was speaking as a review of the County Donegal diocese found "a significant level" of clerical abuse cases in past decades
Six reports published by the Catholic Church in Ireland have revealed there were child abuse allegations against 85 priests across the dioceses.
The audits of child protection practices – two of NI dioceses – were conducted by the Church’s National Board for Safeguarding Children.
They covered the period from 1975 until the present.
The bishop of Raphoe apologised for "poor judgements" in managing priests accused of "horrific acts of abuse".
Bishop Philip Boyce was speaking as a review of the County Donegal diocese found "a significant level" of clerical abuse cases in past decades.
The case of Father Eugene Greene, the convicted paedophile, stood out.
Maeve Lewis, of the abuse victims’ group One in Four, said: "The audits show that real progress has been made in putting in place child protection measures in the six dioceses."
However, she expressed concern "regarding the number of priests against whom allegations have been made who are still in ministry".
Patrick Corrigan, Northern Ireland programme director of Amnesty International, said: "What we can see today is barely a glimpse into the horror of abuse suffered by children in parishes in both Northern Ireland and the Republic of Ireland.
"Clerical abuse survivors in Northern Ireland have been in touch with Amnesty and have told us they wish to see a proper, independent public inquiry into clerical child abuse in this jurisdiction."
A report for the Derry diocese said it had dealt with allegations of sex abuse against 23 of its priests.
A total of 31 allegations had been reported to the police in Northern Ireland and the Republic of Ireland.
The report said 33 allegations had been made to social services.
A total of four priests against whom allegations were made had left the priesthood or were ”out of ministry".
The Derry report said: "Those who have suffered child abuse should receive a compassionate and just response and should be offered appropriate pastoral care to rebuild their lives.
"Those who have harmed others should be helped to face up to the reality of abuse, as well as being assisted in healing."
However, John Heaney, 53, who was abused by other children at a home run by the Catholic Church in Derry, said the review was "a PR exercise by the Church to get people back into Mass".
"It’s a disgrace, this is only about saying ‘look at what we’ve put in place, look how great we are now’. Well it’s too late, not even a hint of an apology," he said.
"If you look at the report, there’s not one mention of prior 1975 victims, there is no mention of any type of help or support for those people still suffering to this day due to the abuse."
Eugene Greene abused boys in the Diocese of Raphoe
The Raphoe report draws attention to "significant errors of judgement" by "successive bishops".
It said "judgements were clouded, due to the presenting problem being for example, alcohol abuse and an inability to hear the concerns about abuse of children".
The review said allegations were made against a total of 14 priests, including Greene, between 1975 and 2010.
Greene, the most notorious offender, was sentenced to 12 years in prison in 1999 for abusing 26 boys over 20 years.
The Irish police received 52 allegations concerning priests in the diocese during the period from 1975 to 2010.
Eight priests against whom an allegation was made are now "out of ministry" or have left the priesthood.
Four have been convicted of abuse. Six priests against whom an allegation was made are in ministry or had retired at the date of the review.
The people of the Diocese of Raphoe have suffered much over the last 20 years with a proportionately high number of priests with complaints of child sexual abuse made against them”
Bishop Philip Boyce
Bishop Boyce said the clergy were "truly sorry for the terrible deeds inflicted on so many by a small minority of priests".
"Insufficient emphasis was placed on the needs of victims, often in the misguided attempt to protect the reputation of the Church", he said.
"This review has concluded that the diocese now has a robust safeguarding policy and procedure in place for safeguarding children."
The bishop said the diocese intended to make renewed contact with survivors of sex abuse to ensure that their needs were met.
"The people of the Diocese of Raphoe have suffered much over the last 20 years with a proportionately high number of priests with complaints of child sexual abuse made against them," he said.
"The number of allegations was also high. It is to our shame that we admit this. But this fact makes us all the more determined to create a safe environment for our children."
The retired bishop of Derry, and former bishop of Raphoe, Seamus Hegarty said: "I now look back and know that my practice in the past was sometimes poor and I am deeply sorry that anyone was hurt through my management of allegations historically.
"I know that I made big efforts to improve as time went on and this is reflected in the Derry report."
In Dromore in Northern Ireland, the audit revealed 35 allegations of abuse made against 10 priests since 1975.
Three of those are now dead and the remaining seven are out of ministry. It said there had been no convictions.
Twelve recommendations have been made, including that Bishop John McAreavey should consider writing to all complainants upon receipt of an allegation, offering them support and counselling.
The bishop said he would "continue to give my best energy to the work of safeguarding in the diocese and in support of all those involved in this crucial area".
The review in the Diocese of Kilmore, which comprises 36 parishes mainly in Counties Cavan and Leitrim – but also in Fermanagh, Meath and Sligo – found there were allegations of abuse against seven priests in the diocese, one of whom is currently in jail for abuse of a minor.
Bishop Leo O’Reilly said: "Each allegation represents a person who has suffered and my thoughts today are very much with survivors of abuse."
The audit on the archdioceses of Tuam was sharply critical of the way in which allegations of child abuse were handled in the past and said "serious harm was done to children by a few priests of the archdioceses".
Twenty-five allegations of child abuse were made against 18 priests of the dioceses since 1975. Two priests were brought before the courts and convicted; 10 of the 18 are now dead – including one of those who was convicted.
The remaining eight are not in ministry.
The report for the Diocese of Ardagh and Clonmacnoise found 14 allegations were made to Irish police concerning 13 priests in the diocese since January 1975 and of those only one is alive and he is no longer in ministry.
One priest was convicted of offences against a child during the period.
There are two other retired priests against whom allegations were made currently resident in the diocese.
All six reports have been conducted by the National Board for Safeguarding Children in the Catholic Church.
In a summary of the findings, the Board for Safeguarding Children said a "marked improvement" had taken place in two key areas.
"Firstly, reporting allegations to the statutory authorities occurs promptly and comprehensively," it said.
"Secondly, the need to create and maintain a safe environment for children in the Church is comprehensively accepted and implemented."
The board helps to protect children in the Catholic Church from being abused by priests or anyone else. It was set up in the wake of various child abuse scandals.
The board is now reviewing every diocese in the country, examining what was done wrong in the past.