Labour MP Eric Joyce called for the resignation of the council's leader and education director following Falkirk's poor performance in examination league tables.
But leader David Alexander (SNP) said education was a devolved matter and Mr Joyce had no right to intervene.
'Eric Joyce would be the first to complain if an MSP started intervening in defence matters,' said Mr Alexander.
Falkirk had received support from local MSP Cathy Peattie (Lab), who is deputy
convener of the Scottish Parliament's education committee, said Mr Alexander.
He also said Mr Joyce had given undue weight to the section of the council's report on part-time employment's effect on pupils.
'The document went into the detail of feedback we had from consultation with schools and parents,' he said.
'Mr Joyce latched onto one part of the report and deliberately took it out of context.'
He dismissed claims the Executive was poised to send troubleshooters into the education department as 'absolute nonsense'.
All education departments would be examined by Her Majesty's Inspectorate, he said, but Falkirk would be among the third tranche of inspections, at the earliest.
'If there was concern about Falkirk at central government level, we would've been in the first tranche,' he said.
But Mr Joyce said it was his duty to intervene to protect his constituents' interests.
'I don't care that it is a devolved issue,' he said.
'Education is the single most important service local authorities provide, and Falkirk is failing.'