Glenthorne Primary School was shut for three months while decontamination took place in 2009. An investigation by the Health and Safety Executive revealed shortcomings in dealing with asbestos both by the council and its contractors, Rugeley-based G Evans (Services) Ltd.
The firm was fined £8,000 and ordered to pay £4,000 costs at Stafford Crown Court.
The firm, in Wheelhouse Road, admitted failing to ensure the safety of persons not in its employment and the safety of persons in employment.
The council, which admitted failing to ensure the safety of persons not in its employment, was fined £10,000 and ordered to pay £5,000 costs.
Judge Mark Eades heard on Friday that the main people at risk from the asbestos were two workers from the firm. Risks to teachers and children in the school at the time were "difficult" to assess.
The court heard the exposure was brief and would not lead to any serious lung problems like asbestosis or cancer.
It happened in February 2009 during the removal of a long wall cupboard, which had to be sawn in half.
The work revealed a foil-lined backing board, which was wrongly identified as non-hazardous insulation material and put in a skip.
Mr Bernard Thorogood, representing the council, said the refurbishment of the nursery was a late addition to the work at the school and the authority accepted responsibility for the failing of a very senior employee.
Mr Stephen Cadwaladr, for the company, said only a small piece of asbestos had been sawn by hand and very few fibres had been released.