Finance boss Cllr Simon Letts said the Government had two years ago said grant funding would be cut by 0.6 per cent in 2013/14.
But he said the council was now bracing itself for an eight to 12 per cent cut when the figure is confirmed next month.
He said the funding cut, worth between £9m and £12m, could have averted any cuts to frontline services.
Council leader Cllr Richard Williams said the worse-than- expected Government grant had made “a difficult job near-impossible”.
Unison branch secretary Mike Tucker said the futures of hundreds of council staff were “being put at risk by the economic policy of the Conservatives”.
Unite branch secretary Mark Wood said it was “absolutely clear that Tory Government imposition on Southampton’s finances is to blame for these massive cuts with George Osborne’s austerity agenda beginning to hit home in a devastating manner”.
Unions have also accused the previous Tory administration of adding to the budget deficit by running down reserves, taking one-off handouts to freeze council tax and saddling the council with interest payments by borrowing for capital projects such as the arts complex and Sea City museum.
But Tory group leader Cllr Royston Smith said the projects were mostly paid for by grants and other funding sources. He said: “It’s nonsense. We left a £6.9m underspend and did not raid reserves. It’s a weak and dishonest argument.”
He said Conservatives would have protected hundreds of jobs by not restoring pay cuts and would have outsourced and shared services to save cash and protect services.
Mr Tucker said the cost of partially restoring staff pay next year, around £660,000, was the same as had been set aside by the Tories for legal compensation for “dismissing the entire workforce and rehiring them on lower pay”.