Will these bugs do great damage?

Thanks for any help you might provide.
After 3 weeks indoors I'm noticing that under the pots (soil) and especially if you tap the pot lightly on the floor, out from the drainage hole come groups of tiny insects maybe 1/10th the size of a grain of rice. I removed a pot from one of the plants and see these insects in or on the soil. So far I do not notice them on the plants themselves. I treated the soil with Neem but looks like it may not have helped at all. These little buggers are proliferating at the bottom of the pots where it meets the soil. Any suggestions?

they are fungus gnats and the larvae will feed on the roots. i get them mostly if growing in miracle grow soil. but i have been noticing a few lately and im using sunshine mix. you can get some of the yellow sticky strips to help with the adult population. i think i have heard a layer of sand on top of your soil will help kill the larvae. but have never tried that. i usually focus on the adults and finish the grow, sanitize everything and start another.