The call from the Scottish Conservatives came after it was revealed that the Scottish Qualifications Authority (SQA) had been bailed out by ministers after recording a £3 million deficit.
The SQA is predicting a similar deficit for 2014/15 - partly due to the rising cost of delivering new school qualifications as part of the Curriculum for Excellence (CfE).
Liz Smith, young people spokeswoman for the Scottish Conservatives, said: "CfE will inevitably stretch budgets, but it is a matter of concern that these budgets are likely to be stretched for the foreseeable future and the Scottish Government is not telling us where the money is coming from.
"At a recent education committee meeting in Holyrood key unions told us that a lot of the work required for the new Higher and Advanced Higher hasn't even been started, so clearly that will add even more pressures. The SQA and the Scottish Government need to come clean on the exact cost of CfE and how it will be paid for."
A Scottish Government spokesman said: "It is not unusual for the SQA to have small variations against budget as so much of its budget is derived from customer income. The position with the SQA was closely monitored and managed throughout the year, in association with the Scottish Government, and a balanced position was achieved at year end."
The financial pressures facing the SQA emerged as thousands of pupils across the country prepare to sit National 4 and National 5 exams from today. The Nationals - which replaced Standard Grades - will be taken by some 54,000 15- and 16-year-old pupils over the next five weeks. In total, more than 147,000 candidates are taking SQA qualifications this year.
Candidates will sit more than 550,000 exams from National 5 and Intermediates to Higher and Advanced Higher, starting today with modern studies.
Dr Alasdair Allan, Minister for Learning, said: "This is a day that thousands of pupils in schools across Scotland have been eagerly working towards throughout the school year. It also marks a new era in Scottish education, with new National qualifications introduced as part of CfE. I extend my best wishes to all candidates preparing for exams over the next few weeks."
As revealed yesterday, minutes of a meeting of the SQA board show the body had an overall deficit of £3m and a cash deficit of £2m in 2013/14. Ministers sanctioned an additional £2m grant.
The SQA has put in place a package of support including extra course materials and hundreds of subject events for more than 7500 teachers. The board papers also warn the quango is facing "significant ambiguity" over its budget for 2014/15 and future years due to the costs of CFE implementation.