Jeff Leaver was speaking after a special meeting to ensure work can start as soon as finance is in place.
It had been hoped contracts for the school could be signed this month.
However, the reclassification of the Aberdeen bypass as a public sector project has had repercussions for a number of other schemes.
Most of the funding for the new learning campus incorporating Dalbeattie High School and Dalbeattie Primary School and nursery is being met by Dumfries and Galloway Council.
Some of it was expected to come from the Scottish government through the Scottish Futures Trust (SFT).
Its "hub" funding model was reviewed by the Office for National Statistics (ONS) after EU rules around publicly-funded building programmes were tightened.
That led to the reclassification of the Aberdeen project and has left the Scottish government to work through "a number of complex issues" with the ONS and HM Treasury.
It has said that it fully expects to resolve the issues but added that there had been some impact on a small number of projects in the interim.
The Scottish government said it was doing its upmost to ensure that delay was "kept to a minimum".
Mr Leaver said the council had taken the project forward as far as it could for now.
"We are very, very disappointed - not just for the council itself but also for the youngsters and the parents and the teachers who are looking forward to moving into this brand new, state-of-the-art school in the next couple of years or so," he said.
"The fact that we don't actually know when it is going to be resolved - that's even more frustrating.
"The schools which we are replacing are not in the best physical condition so what we don't want to be doing is spending even more money patching them up while we are waiting for this to be resolved."
A delay due to funding issues with plans to build a Dalbeattie learning campus has been branded "frustrating" by an education committee chairman.