Helen Law, education spokeswoman for the Convention of Scottish Local Authorities, dismissed the latest statistics as "apples and pears figures" and accused the Tories of using different sets of statistics to produce a misleading headline figure.
Brian Monteith, the Tories' education spokesman, believes the figures underline the need to allow headteachers to buy in services and free them from restrictive local authority shackles.
"The total sum of money failing to reach schools is truly astonishing and will come as a shock to many in Scottish education, except possibly headteachers," Mr Monteith said.
National figures appear to show that the average percentage of cash devolved to headteachers is just 70 per cent. But Andy Anderson, Highland's education convener, said the Tories' figure of 59 per cent for his own authority was out by 25 per cent.
"Their figures are suspect," Mr Anderson said. "We are reaching 89 per cent of budget and devolving even more to heads."
Fraser Sanderson, the education directors' president, said money not devolved was still spent on young people, while items such as transport and school meals could not be realistically passed on. Cash was not "squirrelled away".