Two judicial reports published in Ireland last year revealed that church leaders had protected child-abusing priests from the law, while many fellow clerics turned a blind eye.
The reports, which shocked the nation, documented decades of sexual, physical and psychological abuse in Catholic-run schools, workhouses and orphanages.
'Pain and anger'
"The bishops spoke frankly of the sense of pain and anger, betrayal, scandal and shame expressed to them on numerous occasions," the Vatican statement said.
The bishops also vowed to co-operate with Irish courts investigating sexual abuse.
Support groups in the United States and Ireland have condemned the talks, saying the pope should go to Ireland to apologise for the abuse.
A US group dismissed the talks at the Vatican as a "carefully orchestrated public relations move".
"Does anyone honestly think that the very same men who ignored and concealed child sex crimes for decades will ... suddenly be part of the solution, instead of part of the problem?" Barbara Dorris of the Survivors Network of those Abused by Priests asked.
She deplored a "centuries-old, deeply rooted culture of self-serving secrecy perpetuated by a rigid, ancient, all-male monarchy."
John Kelly, the founder of the Irish Survivors of Child Abuse group, said: "The Irish people and the victims are entitled to expect firm actions from the pope.
"Tomorrow is the beginning of Lent, time of penance, and we must begin with ourselves"
Cardinal Sean Brady, archbishop of Armagh
"We are entitled to expect that the pope make those who committed crimes or covered up crimes, including bishops, be made accountable," he said.
"The words coming out at the moment seem to be positive. Whether they will act upon them and whether they will go far enough is another matter. We need to see the words turned into action."
Ireland's crisis was followed in January by a scandal in Germany, where officials of an elite Jesuit school in Berlin admitted there had repeated sexual abuse of teenagers by teachers in the 1970s and 1980s.
Four Irish bishops have tendered their resignations over the Ireland scandal but only that of former Limerick bishop Donald Murray, who was deputy bishop of Dublin from 1982 to 1996, was effective as of the Vatican visit.
One of the four, James Moriarty of Kildare and Leighlin, attended the talks at the Vatican.
The Irish delegation that met the pope was led by Cardinal Sean Brady, archbishop of Armagh and primate of all Ireland.
Brady acknowledged leadership "failures" in the handling of the scandal following the talks with Benedict.
"There have been failures of course in our leadership, and as one of the victims' daughters said, the only way we will regain that credibility is through our humiliation," he said.
"Tomorrow is the beginning of Lent, time of penance, and we must begin with ourselves."
The Vatican said the pope planned to issue a pastoral letter to Ireland's Catholics over the scandal.
The letter will be aimed at "restoring confidence" among Irish Catholics and to offer "concrete and effective" ways to prevent a recurrence, a Vatican expert wrote in the Italian newspaper Corriere della Sera.