Councillor Gary Womersley added that the council would be left to "pick up the pieces" of the controversial tax.
Under the new 'bedroom tax', families on housing benefit will be assessed for the number of bedrooms they actually need. The UK government has claimed the upcoming change to the welfare system will help cut the annual £23m bill for housing benefit.
The new tax affects housing benefit which is paid to less well-off tenants to help with rent and families which are deemed to have too much living space by local authorities will receive a reduced payment.
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Councillor Womersley said the legislation would have a real and long-term damaging effect on many of the most vulnerable in society and put even more strain on local government services that are already creaking under pressure.
He said: "It is ironic that the first batch of these welfare and benefit reforms come into force on April Fools' day, because, believe me, there is nothing remotely humorous about them.
"Our role in this is to manage the consequences in the way that does the least possible damage to our communities and that will be a very, very difficult task.
"No part of my speaking out on this issue should be seen as a suggestion that we do not embrace change or that we do not recognise the need for some change within the current system. Indeed we've shown at Clackmannanshire Council we can both improve services and reduce costs."
The Department for Work and Pensions has insisted the changes are required in order to bring "fairness back to the system – when in Scotland there are many thousands on housing waiting lists or living in overcrowded homes".
(JP)
