Dr Denis Brennan, from Ferns in Co Wexford, said the appeal was not about sharing the blame but asking for help to meet responsibilities.
He said the abuse scandals and subsequent cover-ups to protect dangerous clergymen were caused by paedophile priests, mismanagement and poor understanding.
"This particular tragedy is not viewed by the diocese as a problem to be solved," the bishop said.
"More accurately, people who suffered abuse are not the cause of our problems: the actions of individual perpetrators, along with mismanagement, poor understanding and/or lack of resolve are."
An inquiry into paedophile priests in Ferns uncovered more than 100 allegations against 21 priests from the 1960s to 2005.
Bishop Brendan Comiskey, who resigned in 2002, was branded negligent while the Vatican was aware of complaints but failed to act, the report found.
Diocesan authorities have paid out more than 8 million euro (£7.2m) in 48 settlements to child abuse survivors.
There are 13 civil actions pending.
It also paid out another 2.1m euro (£1.9m) towards inquiries and 836,000 euro (£756,000) towards the treatment of paedophile priests.
"The settlements made to date are necessary and represent the diocese's desire to take responsibility for hurts caused, hurts which date back several generations - as far back as the 1940s in cases," Bishop Brennan said.
He made the appeal for funding to parish representatives at the diocesan AGM in Enniscorthy on Monday night. He said the diocese had been on a road of settlement of claims for 15 years.
"Funding sought is not about sharing the blame, it is about asking for help to fulfil a God-given responsibility," he said.
"'That I did not cause the problem' is not the response of the Christian, 'that I would like to help in the work of justice, healing, reconciliation, a safer environment for children in the future, proper financial stewardship and overall good economic health' is.
"I would be grateful for whatever ways you might be able to help me and the diocese to complete a road on which it has been necessary to travel, a road that will hopefully go beyond the requirements of justice and grow in terms of the reconciliation with which we are currently engaged and may be further permitted, or invited, in the future."
+++++++++++++++++++++++++++++++++++++++++++++
Disclaimer
No responsibility or liability shall attach itself to us or to the blogspot ‘Clerical Whispers’ for any or all of the articles placed here.
The placing of an article hereupon does not necessarily imply that we agree or accept the contents of the article as being necessarily factual in theology, dogma or otherwise.
SIC: BT