Trying to provide fertility via soil for a potted plant is impractical because the small, closed environment can't sustain the microbes necessary to convert/process organic material into a form that plants can use. Also too easy to accidentally radically alter the PH, or create other wild imbalances that could make plants ill. Making a compost tea with which to water is much more likely to do wonderfully good things for potted plants.
If you're interested in and able to repot a couple times per year, depending on conditions, fertility-via-soil could show decent results, assuming the particular plant liked the particular mix. But becoming too wet, dry, hot, cold, just once could kill the microbes.
I usually don't even compost the materials first to do a compost tea, just put them in my water bucket (at least overnight,) use the water for thirsty potted plants, then dump the contents on the ground in a bed where they can decompose and become part of the mulch. (Before I gave up on pile composting, the contents would have been dumped on the compost pile at that point.)
Anyone even remotely interested in having "good dirt" for plants should enjoy this short lecture, (though it doesn't discuss potted plants at all):
http://permaculturenews.org/20...
Edited to say, forgot to say before, KUDOS to anyone trying to compost in an apartment!