But Martin Crewe, the director of Barnardo's Scotland, argued the losses would be worth it in the long run if the concordat, which removes ring-fenced funding streams, allowed councils to plan strategically and reduced the bureaucracy that comes with ring-fencing.
"If you are standing back and saying: 'What's best for Scotland?' then taking off the ring-fencing makes perfect sense," said Mr Crewe. "But when ring-fencing comes off, if you're a cash-strapped local authority like Edinburgh or Aberdeen, you are going to re-prioritise and that money may simply be withdrawn."
One example of a vulnerable project might be his charity's Lighthouse project, which aims to prevent teenagers who have committed serious sexual offences from re-offending. However, as it is funded using a specific stream of funding - the Youth Crime Prevention Fund - Edinburgh City Council could decide that money would be better spent elsewhere in April.
His comments came as MSPs on the parliamentary education, lifelong learning and culture committee turned up the heat on the local authorities, demanding to know what Scottish councils would choose "not to do", now they have considerably more spending freedom.
Under the concordat between the Scottish Government and the Convention of Scottish Local Authorities, in exchange for freezing council tax, ring-fenced funding has been reduced considerably. For its part, local government will have to deliver a series of outcome agreements.
Karen Whitefield, the committee's Labour convener, asked Cosla officials: "Ring-fencing has been removed from the fund for raising educational attainment for looked-after and accommodated children - how will your organisation guarantee that local authorities will fund that provision? In the past few years, for the first time, that fund has guaranteed that some of the most vulnerable children in Scotland have access to the same amount of books and materials that other children in Scotland take for granted."
Jon Harris, Cosla's strategic director, said that individual councils would decide where money was spent, adding that "local authorities are well aware of the priorities of looked-after children and of their role as a corporate parent".
The Scottish Council for Voluntary Organisations, like Mr Crewe, welcomed a less "nannying approach", but said charities were concerned that the agreed outcomes were not comprehensive enough. It added that organisations like the Prince's Trust Scotland, which supports youngsters in danger of being turned off from education, were concerned about the prospect of having to negotiate with 32 local authorities instead of one at a national level.