@bluter and
@Phytoplankton already covered it but I’ll reiterate because it is that important. As long as they’re not sat directly on the concrete you’re good. You could get away with simply laying a blanket on the ground if it was that dire.
If you’re gonna run fabric pots I would recommend something along the lines of the boards, a pallet, 2x4s, etc. just something that will elevate the containers but allow air flow underneath.
If I could run in a basement/cellar I would prefer it but my current house only has a crawl space so I’m forced into the attic. Basements/cellars can keep a pretty consistent temperature regardless of the outdoor weather. In my attic I’m constantly battling the weather more than anything else