Cosla said essential services have been left in a "precarious position".
Councillor Gail Macgregor, its resources spokeswoman, said the funding outlined in the Scottish budget represented a £100 million cut.
She welcomed the SNP' s decision to end its long-running policy of freezing or placing a cap on council tax rises, but added: "We cannot put the burden of a poor settlement onto hard pressed families. That is simply not fair."
SNP Finance Secretary Kate Forbes was accused of opening the door to "massive" council tax hikes after she delivered her budget on Thursday.
She insisted the spending plan deliver “real-terms growth" for councils.
She added: "It protects the core budget in cash terms and it also ensures that local government are getting a fair share of the health and social care consequentials, which is something that they have long called for."
But in a damning statement, Ms Macgregor said: “We wanted a budget for local government that enables people to live well locally – what we have is a budget that barely allows local government to survive.
“We are left in a position where we do not have adequate funding to provide our range of essential services and support recovery from Covid.
“Many essential services provided by Scottish local government are in a fairly precarious position as a result of cuts to councils’ core budgets and direction on spend towards Scottish Government priorities over the last few years."
Cosla president Alison Evison said: “The Scottish Government has to realise that cuts to our core budget hit the most vulnerable in our communities the hardest and are damaging to our workforce.
“That is why council leaders were unanimous today that we must fight for a fairer settlement.
“The consequences of us not doing this would be disastrous for our communities and workforce."
Scottish Conservative MSP Miles Briggs earlier accused SNP ministers of “passing the buck to councils” to make up for a funding shortfall.
He said: “Everything Kate Forbes has done regarding council tax is cynical and calculating - but, ultimately, it’s the public who will pay, either through poor local services or huge council tax rises.”