Derek Vaughan (Lab), leader of the Welsh Local Government Association, said the move amounted to 'robbing Peter to pay Paul'.
'The assembly deliberately takes£15m out of school budgets every year for efficiencies,' he said.
'Its announcement [now] forces councils to put back into schools what the assembly government has previously taken out.
The budget followed complex negotiations after the other parties combined to thwart the assembly's minority Labour administration's original proposals.
Finance minister Sue Essex said she had taken£14.4m from reserves to spend more on services, including school energy costs, foster care and fire fighters' pensions.
She warned that reserves would fall to only 1% of the assembly's budget, which she called 'the very minimum considered necessary not to put public services at risk'.