Without further info, I'd guess that the potting mix is probably on the wet side which is more of a problem for the plants than the white things.

There are a number of discussions on controlling pests in containers over on the Container Gardening forum here. They may be of help to you.

Otherwise, as Jean said, without identifying the specific pest involved it is difficult to offer a solution. Container soil that is kept too moist is a magnet to many different pests including aphids, spider mites, gnats, fruit flies, scale, and even thrips or weevils. The harm done depends on the degree of infestation but controls for most all are available.

Dave