Environment secretary David Miliband outlined a plan for councils to decide extra charging, fines and discounts.
Mr Miliband also asked councils to collect food waste separately.
But the strategy left key questions unanswered said the Local Government Association.
'Councils have argued for an urgent and radical overhaul of the amount of rubbish produced and the way in which it is thrown away,' said LGA chairman Sandy Bruce-Lockhart.
'Councils need more money to pay for dealing with waste. The strategy sets out plans to almost double recycling targets which will be impossible to achieve without proper government investment.'
New Local Government Network said that charging could be a useful tool to ensuring councils avoid EU penalty fines on recycling, the impact of which could push up levels of council tax.
Communications head James Hulme said:
'Councils are under pressure to enforce tough EU targets on recycling and it is clear that doing nothing is not an option.
'Increasing sources of income for councils through charging for services could help to take the pressure of council tax and limit the need for above inflation rises; however it is important that councils do not see charging as a vehicle for increasing the tax burden on households'.
The Liberal Democrats said the strategy was too little too late.
'We have the third worst recycling rate in the EU, and ministers are still far too unambitious,' said environment spokesman Chris Huhne.
'We need a right to return excessive packaging at retailers, trials of a plastic bag charge plus more prosecutions for excessive waste and fly-tipping.
'We oppose new waste tax powers for local councils, but would welcome schemes which give rebates on council tax for residents who recycle. We don't need 'pay as you throw', but councils should be able to give 'rebates as you recycle'.'