It follows the announcement of its provisional local finance settlement, which is due to be finalised over the coming weeks.
Announced on 19 December, the provisional settlement included a £15m increase in the Rural Services Delivery Grant (RSDG).
See also: More must be done for fairer rural deal
Although the increase irons out the anomaly of a reduction in 2018-19, the Rural Services Network said it was more symbolic than making a huge difference.
RSN chief executive Graham Biggs said it was important to note that only "super sparsely populated" local authorities would receive the RSDG grant.
Other rural authorities, which wouldn't receive the grant, also faced higher costs associated with providing public services to sparsely populated areas, he said.
Cornwall Council said the government had to recognise local budgetary pressures and the “massive strain” being placed on local services.
Council leader Adam Paynter said “Councils have absorbed a massive share of spending cuts from central government, leaving many of our services under acute pressure.
“This pressure will only continue as the central government grant reduces even further by 2019/20.”
Adult social care and services for vulnerable children and families are under real stress due to increasing demand and reduced funding, said Mr Paynter.
“Our current budget consultation shows the challenge we face in finding the funding gaps for these critical services, as well as cleaning streets, collecting rubbish and recycling, and fixing potholes.
“Already we have to find £75m is savings over the next four years.”
Lincolnshire County Council leader Martin Hill said the money it received from the government was continuing to fall.
Yet at the same time, local authority costs were being pushed up by inflation, an ageing population and the national living wage.
In total, the authority's estimated budget shortfall for 2017/18 stood at £60m, and difficult decisions would be needed in the weeks and months ahead.
In a New Year message, Mr Hill said: “Councils across the county have received far less money than metropolitan urban areas.
“We believe that supporting our communities across a sparsely populated rural area provides its own challenges and that we should be funded by central government accordingly.
“We are actively lobbying alongside our MPs for the funding system to be reviewed.”
North Yorkshire County Council said the provisional settlement left the local authority with a “very difficult choice”.
It could either take up the government's offer to increase council tax by a further 1% or make further cuts which would impact on frontline services.
The government has given local councils the opportunity for an additional increase of one per cent on council tax without triggering a referendum.
People in North Yorkshire already paid almost twice as much council tax in relative terms as those in urban and received less government funding – yet the costs tend to be higher.
Moreover, by April 2019 the council was due to receive no core government funding whereas some councils would continue to receive significant levels of government money.
“This settlement does nothing to fix that fundamental disparity”, said Gareth Dadd, North Yorkshire’s deputy leader and executive member for finance.
Cambridgeshire County Council Steve Count said the government's funding formula was “seriously undermining” the local authority's ability to deliver services.
County councils received an average of £292 per resident less than councils in London and £166 less per head than metropolitan boroughs.
At the same time, levels of demand were rising faster in rural areas than those in more urban areas.
Cambridgeshire was the fastest growing county in the UK – yet it was third from the bottom out of a total of 27 Shire counties in the funding received from government.
If Cambridgeshire received the average level of government funding (RSG) for counties it would receive an additional £13.7m each year to spend on vital frontline services each year.
If it was funded to the level of the average London borough it would receive an extra £75m each year, said Mr Count.
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