The warning comes after the Scottish Qualifications Authority (SQA) introduced charges for the first time to cut down on bogus appeals as part of a wider shake-up of the system.
The new costs will range from £10 for a check to see if the marks have been added up correctly to £39.75 for a full review of the marking. No charge will apply if a mistake has been made.
The SQA has said it is up to local authorities to decide whether the costs are paid for out of central funds or taken from school budgets, but headteachers' union School Leaders' Scotland said a postcode lottery could result.
Ken Cunningham, the organisation's general secretary, said he supported the introduction of the charges, but was against schools paying them.
"If individual schools have to pay, that could lead to inequalities in the system because some schools would be able to afford it and others would not," he said.
"That would be unfair. We have to watch carefully that youngsters are not deprived simply because of where they find themselves."
Liz Smith, young people spokeswoman for the Scottish Conservatives, called on the Scottish Government to issue guidance on who should pay the charges.
"With the introduction of the new National exams it's inevitable that there will be more requests for marking reviews this year," she said. "I'm worried that if schools get the bill that will act as a disincentive, when these decisions should be taken based on academic merit."
An SQA spokeswoman said: "We expect requests for clerical checks and marking reviews to be made only if the school or college is confident this is the case."
Bruce Robertson of the Association of Directors of Education in Scotland added: "We would not want to see any pupil disadvantaged and if there are good, well-thought-through grounds for a review then the school should go ahead, but the days of mass speculative appeals on grades are over."
The move by the SQA, announced two years ago, has been broadly welcomed, with many agreeing the old system was used too widely by schools.
Last year, the SQA received 67,000 requests - meaning about 7% of exam entries were appealed - but fewer than half were successful and the process cost the body almost £800,000.
The system was originally intended as a safety net for exceptional cases, but in recent years has become widely used for pupils who "had a bad day" in the exam.
Under the new system there will be two options: the exceptional circumstances consideration service and the post-results service. The first of these is free and is to be used by schools in cases where they believe, for example, that a candidate has suffered because of bereavement or illness. Schools will be able to submit a wider range of evidence than in the past to support these claims.
However, if a school is concerned about a candidate's result and wants to ensure that no errors were made during marking, there will be a charge if the grade remains the same once checks have been carried out.
Edinburgh and Glasgow city councils and Borders council said they had yet to reach a policy decision on who would meet the cost of the new charges.
However, it was likely Glasgow schools would use their devolved budgets to pay for unsuccessful review requests, the city's director of education Maureen McKenna said. She added: "Our schools would not allow an inequity to arise and neither would we."
A spokesman for Fife Council said the cost would be covered centrally.