Labour directed the accusation at the Education Secretary as it also emerged that the Scottish schools inspectorate had deleted information on historical school inspections.
Yesterday Mr Swinney struck a compromise deal with local authorities on one of his key education proposals – his plan to set up regional bodies to support school improvement.
Originally Mr Swinney had wanted the heads of the new bodies to be accountable to Education Scotland and the Scottish Government, raising concerns that the democratic role of councils would be bypassed.
But under the new deal each local authority will be part of one of six regional “Improvement Collaboratives” in partnership with Education Scotland, which will be accountable to the councils taking part.
The about-turn came as figures provided by universities showed that more than 200 places on post-graduate teacher training courses for secondary subjects have not been filled. The number of vacancies is the equivalent of a quarter of the total.
The courses started last month but almost four in ten places for English have not been taken up. There are also shortfalls in music, biology and modern language courses.
Meanwhile, Education Scotland has been accused of a “wilful attempt to frustrate transparency” after it emerged the organisation no longer had information relating to school inspections carried out before 2008.
It has also started deleting school inspection reports that are more than five years old from the publicly accessible section of its website.
Labour education spokesman Iain Gray said: “This is humiliating for John Swinney. This is not an instance of one policy failure, but rather an omnishambles across the education portfolio.”
Mr Swinney said he looked forward to national and local government working together “at pace” on his reforms.
“I look forward to national and local government working together at pace – with support and expertise from Education Scotland.”
A Scottish Government spokeswoman said ministers were “committed” to ensuring there were the right teacher numbers. On the loss of inspection data, the government expected public bodies to have “robust” data management.