Stevens was responding to the Scottish Government's refusal to renew a £350,000 grant to run CSV's retired and senior volunteer programme, known as RSVP, which was debated in the Scottish Parliament last week.
She said £60m of the Scottish Government's £90m budget for the voluntary sector in the current financial year would be spent on social enterprise.
"The SNP administration needs Scotland to be economically stronger if there is to be any hope of it becoming independent, and it sees social enterprise as a way of doing that," she said. "It is good for social enterprise that it is getting more attention than ever, but those that aren't social enterprises are concerned the Government doesn't place the same value on the work and services of the vast majority of the sector."
Jim Mather, minister for enterprise, energy and tourism in Scotland, said the ending of central funding for RSVP was a consequence of the Scottish Government's new arrangements with local authorities, under which many funding decisions are devolved to the authorities.
He said: "We are dealing with an evolutionary process, and I expect something to evolve that is based on sound roots, is much stronger and is more effective on a totally different and larger scale."
But Stevens said the RSVP decision had nothing to do with the new political arrangements. She said: "This is a policy decision by the Scottish Government. It thinks everything the voluntary sector does should be local so it is appropriate for funding to come locally, but it hasn't given local authorities any more money."
She said the RSVP programme had been of such high quality only because it had benefited from CSV's national infrastructure.
Jack McConnell, Labour MSP and former First Minister, said: "When relatively small sums of money are involved, the amount of time and effort that voluntary groups have to divert from core activities to the pursuit of grant funding from 32 different local authorities would be far better spent encouraging volunteers in the community."
A spokeswoman for the Scottish Council for Voluntary Organisations said it was working closely with CSV to help the RSVP programme make the transition to the new arrangements, which had "made the future very uncertain for many Scottish voluntary organisations".
Andrew Jackson, media and public affairs manager for Scotland at volunteering charity WRVS, said: "We would not wish to see well run, socially important volunteering initiatives disappear as an unintended consequence of arrangements made between central and local government to improve public services."