Archbishop Mario Conti said he had been "blindly satisfied" in the past that youngsters were being properly cared for at Nazareth House in Aberdeen, the city where he became a bishop in 1977.
The 84-year-old clergyman expressed his "pain and sorrow" to those who have suffered mistreatment and later issued a statement saying he stands with "all those who have been abused".
And the former church leader - who has faced criticism from some survivors for past comments about the allegations - asked for their forgiveness "if they feel I was insensitive to their pain".
The Scottish Child Abuse Inquiry was also told he believes allegations of a cover-up by the Catholic Church are unfair.
Over the last eight weeks, the probe has been looking specifically at the now-defunct children's homes run by the Catholic congregation the Sisters of Nazareth in Scotland, including one in Aberdeen.
The inquiry has been told of a string of alleged abuses by nuns at those institutions decades ago.
On Tuesday, the probe was shown a BBC documentary from 1998 on the allegations of Nazareth House survivors.
Archbishop Conti said he was "horrified" by some of the claims.
He told the inquiry: "I am deeply ashamed of what has been revealed and I express my pain and sorrow to those who were abused.
"Clearly all we are doing (in the inquiry) is an attempt to get to the truth and provide an opportunity for some redress at least in terms of saying sorry to those who have had bad experiences.
"I hope they will find it in their hearts to forgive their abusers and to forgive me if they feel I was insensitive to their pain."
Earlier this year, a lawyer representing the group In-Care Abuse Survivors (INCAS) told the probe of a letter from the then Bishop of Aberdeen in which he appears to refer to survivors as "the opposition".
Archbishop Conti began his religious work in Aberdeen in the 1960s and went on to become the Bishop of Aberdeen and, later, the Archbishop of Glasgow, before retiring in 2012.
He told how religious orders worked independently, without interference from bishops, but that he was "engaged pastorally" with Nazareth House in Aberdeen during his time in the city.
Colin MacAulay QC, senior counsel to the inquiry, asked whether he had been satisfied the children
at that Nazareth House were being properly cared for.
"Yes, blindly satisfied, because I wasn't seeing what now has been revealed," the churchman replied.
He told how he was "taken aback" when two police officers first told him about allegations of abuse at the home.
"I said 'I think you'll find that is not the case'," he told the probe.
Archbishop Conti told how he felt "shock but also disbelief" as allegations of the mistreatment of children escalated towards the end of the 1990s.
He told how the general discipline standards of the time now shock people and claimed some "fantastical" allegations "made people question the veracity of those that had genuine experiences".
Of the other claims, however, he told the inquiry he was "here today, apologising for what we now know to be truthful".
Mr MacAulay also read from the Archbishop's written statement submitted to the inquiry, in which he described allegations of a cover-up of abuse claims by the church as "unfair".
"There was this natural instinct on the part of the church to solve problems in a pastoral way," it said.
In a statement issued following the hearing, Archbishop Mario Conti said: "My evidence today gives me the opportunity to state that I stand with all those who have been abused and express my pain, sorrow and profound regret that this should have happened to them."
He added: "Cruelty is more than lack of affection. Even one case of child cruelty would be one too many.
"With evidence of many cases offered to the Inquiry I can only feel considerable revulsion and I join my apology to that already made by Archbishop (Philip) Tartaglia to all who suffered in any way in any Church institution."
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