Pictures really help with identifications. 'Looks like' descriptions are often misleading.

I'd compare aphids to what you're seeing and Black Sooty Mold (caused by insects such as aphids, scale, mealies, etc.

Perhaps lacebugs, one of the most common pests of asters.

You have described what I'm seeing on my asters now. The bugs look like small grey mealybugs. I sprayed them with sevin twice already, they're persistent.