Cosla said the Scottish Government’s spending plans over the next four years are “deeply concerning for communities across Scotland”.
Council workers are being balloted for a strike over pay in a move unions warn could see school closures and waste “piling up on the streets”.
The Unison, Unite and GMB unions have rejected a “paltry” 2 per cent pay offer from Cosla.
The council body said it was “deeply disappointed” that Ms Sturgeon and finance secretary Kate Forbes had refused a request to discuss the financial settlement facing local authorities “and its significant impact on our ongoing pay negotiations”.
There are rising concerns about strikes and industrial unrest following a breakthrough in the pay dispute between ScotRail, which was recently nationalised, and its train drivers.
Negotiators for Aslef, the union representing drivers, recommended acceptance of an improved 5 per cent pay deal after weeks of rail disruption.
Other unions say this raises the bar for their members, who are pushing for better offers in the face of high inflation and the cost-of-living crisis.
From Monday, ScotRail will reintroduce services on some routes, a move which will see the last train home for many leave later.
However, it still faces the prospect of industrial action, with the RMT union, which represents conductors and ticket examiners, yet to accept a similar deal to Aslef.
Meanwhile, teachers have also rejected a 2 per cent pay offer.
Larry Flanagan, the outgoing general secretary of the EIS teaching union, told its annual general meeting in Dundee: “Cosla and the Scottish Government are on notice that come the autumn, we will be strike ready if required.”
The Government’s recent resource spending review, which sets out its broad spending plans for coming years, outlined more than £1 billion of real terms cuts for key areas including councils and the police.
Cosla said this had “further increased the already strong likelihood of industrial action in the coming months”.
In a statement, it said: “[The] Scottish Government continues to fail to respect the fundamental role local government and its workforce has in addressing their own priorities of tackling child poverty, climate change and a stronger economy.”
It said the resource spending review showed council funding “will remain static at a time when inflation and energy costs are soaring”.
Cosla added: “This ‘flat-cash’ scenario gives no scope to recognising the essential work of our staff, whose expectations, quite rightly, are being influenced by Scottish Government’s decisions in relation to other parts of the public sector.
"A suggestion that increases in welfare payments will mitigate the cost of living crisis do not recognise that our staff should not have to depend on such payments to make ends meet.
"As things stand, the only option available to councils is yet fewer jobs and cuts to services that are essential to communities everywhere.”
Gail Macgregor, Cosla's resources spokeswoman, said: "No increase in our core funding damages these services and limits the options we have in successfully concluding pay negotiations.
"Refusal to engage in discussion will only see this continue and our communities will see and feel the difference."
Scottish Conservative local government spokesman Miles Briggs said: “Local councils provide a host of essential services, so it’s deeply concerning for the public that so many staff are contemplating strike action over the coming months.
“Amid a global cost-of-living crisis, it’s understandable that workers are seeking healthy pay rises to compensate.
“These requests will be tough for any employer to meet, but especially for Scotland’s councils, which have been systematically underfunded for years by the SNP Government.”
A Government spokeswoman said: “Pay settlements for council workers, excluding teachers, are a matter for Cosla and are determined through negotiations at the Scottish Joint Committee (SJC).
"As it is not a member of the SJC, the Scottish Government cannot intervene in pay negotiations, which are for the trade unions to negotiate with Cosla.”
She said the overall Scottish budget fell by 5.2 per cent in real terms between 2021/22 and 2022/23, and stressed the resource spending review “does not replace” the annual budget process.
The spokeswoman said: “Annual budgets for portfolios, local government and other public bodies may therefore vary from those set out or implied in the spending review, particularly once transfers to local government from other portfolios are taken into account.”