Actually, yes, the way you would treat that is to use a suede brush with a suede eraser. You can get one of those almost anywhere that sells shoe cleaning supplies. Remove the stains as much as possible with the eraser part, and then use the suede brush to pull the nap back up and make it fuzzy abnd even again. Coach used to sell the best suede brush eraser combo ever, but no longer. I got mine at Target, and it has nylon brushes, which I don't really like. The Coach one had metal bristles that worked much better.
Here is a link to pics of my suede brush on my blog:
http://coachbagrehab.blogspot.com/2012/05/suede-brush.html
And even one of those brass bristled brushes sold in autmotive with the tools might work better than the nylon one I have, just go slow and be careful! You don't want to use a brush that is too rough and poke a hole in your purse by accident!!
And, someone actually has a listing up for a Coach one, I can't see if the bristles have any metal ones mixed in, but it might be the best option:
http://www.ebay.com/itm/COACH-SUEDE...ltDomain_0&hash=item4603f2398d#ht_3083wt_1344