Brian Wilson, the Education Minister, and the Convention of Scottish Local Authorities blamed the failings on the nursery voucher scheme, which the Government has reluctantly been forced to continue. Vouchers have, however, been abandoned in Wales.
Mr Wilson said: "The gaps in provision fully justify the Government's scepticism towards a voucher-based system and its determination to replace it with a commitment to universal provision."
Alex Thomson, Cosla's education convener, said: "We warned that nursery vouchers would not provide a solution to finding pre-school places when they were introduced and I am not at all surprised by the minister's comments.
"Cosla is clearly of the view that the needs of pre-school children should not be left to either the bureaucracy of vouchers or the inconsistencies of the supply and demand of the market-place. Pre-school provision should be planned by councils, guaranteeing a place, choice and quality for every four-year-old, as well as a smooth transition to primary education."
The Scottish Office has now issued a list of 2,200 registered centres that qualify to take part in the final year of nursery vouchers, of which 1, 261 are local authority nurseries and 945 are private, voluntary or independent.
Councils are being urged to study the list carefully and liaise with voluntary and private sector providers to close the gaps. Mr Wilson said it was "unrealistic at this juncture" to expect education authorities to create all the additional places for the coming session.
Two weeks after the election, the minister announced that the scheme would run for a final session because of the complexities in dismantling it. The administration has, however, been simplified. There will only be one issue of vouchers and the number of signatures required from pre-school staff has been cut by almost a million.