I battled the fungus gnats all last winter, it was a terrible infestation. Part of the problem was using air pots instead of the fabric bag pots, the gnats used the holes in the side of the pots like Hotel California. I went back to fabric pots.
I ended up using mosquito nets just like the picture above, which did help contain the flying gnats, but they are still active inside each mosquito bag, and that doesn't kill the eggs which hatch into larvae and do the damage. For that, you need mosquito bits, 4 tablespoons per gallon of water. That stuff does work but it takes several water cycles.
In the meantime, you need to contain the flying gnats or they will keep laying new eggs. Instead of mosquito bags, I cut pieces of fabric from one of the fabric pots and cover the top of the soil with the fabric. The soil will still breathe just fine, and the gnats can't get in and out. You can water right thru the cut in the fabric, just remove and replace the tape. Leave some excess to tuck the sides in all the way around. You may want to put something on top of the fabric to hold it down between watering, if necessary.