Speaking on RTÉ's Morning Edition, Mr Quinn said the religious bodies would not accept the principle of 50-50 under the State-backed redress scheme.
He said the State had spent around €1.4bn on legal costs and awards relating to abuse at residential institutions to date.
Mr Quinn said as a result of paying this money out, and the inability to get the Church to contribute an equal share, everything else must be considered when it came to reducing expenditure at the Department of Education.
The State established the Residential Institutions Redress Board in 2002 to make compensation payments to former residents who were abused.