Their calls for a cross-party investigation were dismissed.
Instead, the reasons behind the roads chaos and major problems with salt stocks will be investigated by Stuart Nichol, chief executive of environment and transport services, and his report
will be put in front of councillors in early March.
The inquiry comes after a number of leading politicians from all parties – including Tricia Marwick, SNP MSP, Conservative MSP Ted Brocklebank, and Alex Rowley, Labour group leader – demanded answers into how Fife almost ground to a halt.
Mark Hood, Labour's finance spokesman, said the review should have been handled independently.
He said: "I was somewhat surprised to read that the executive director who is in charge of winter maintenance is to carry out an investigation into his own services' performance.
''I would think the public would at the very least expect some kind of neutrality – it is very difficult to see how this would be achieved when it is being carried out by the man who occupies the job with ultimate responsibility for winter maintenance".
But the structure was defended by the administration which said it followed the same format as previous post-emergency reviews.
Councillor Tony Martin, chairman of the environment, enterprise and transport committee, said the review was being held in the same manner that post-emergency planning reviews had been held in the past.
He added: "I have every confidence that this will be a proper and thorough review of the way we have handled weather issues over the last few weeks."
The announcement came after the council denied rumours it had cancelled a delivery of salt in light of predictions of a mild winter.
Ayrshire-based Peacock's Salt, the company which provides Fife with its supply, hit back last week after the council laid the blame for the shortage at its door. The company claimed it had warned its customers of a shortfall as long ago as July.
Dr Bob McLellan, head of transportation services, said: "The contract is done on the basis that they (the company) have to have a minimum level of stock in at any time – and that stock should be the absolute minimum they can have.
"They should have had 5000-8000 tonnes for us, in reality it was less than 2000 tonnes.
"The report that Peacock said it warned us in July is neither here nor there. Its obligation is to the client and if it had fulfilled the terms of its contract, we would have the salt that we ordered."
He added: "As far as questions about how much salt we had to begin with, we had 20 per cent more in stock than the previous year because last year we reviewed the stock levels after a shortage last winter."
Want to comment? E-mail
efmeditor@fifetoday.co.uk