Store bid rejected
North Lanarkshire Council said the loss of some 90 car parking spaces at the shopping mall would be unacceptable.
But the shopping centre's managing agents said an opportunity had been missed to boost the local economy by increasing footfall.
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Hide AdThey have not ruled out either an appeal or an amended application.
Simon Usher, asset manager at La Salle Investment Management, said: "We are looking at all the options. We are certainly reviewing our position at the moment."
He insisted the supermarket, which it is understood would have been leased to the Aldi's chain, would have been of benefit to the town centre.
"It would have generated an extra reason for people to visit the town centre of Cumbernauld," he said.
The application included a plan for a betting office.
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Hide AdBut planners said the loss of 92 out of 175 well used parking spaces serving the ground floor shops would be detrimental.
While 94 new spaces were proposed through a basement car park and a reconfiguration of the roof top car park, there would still be a shortfall of 81, given that new spaces would be required for the extra shops.