Depending how deep the pile is,can you use very sharp nail scissors and gently cut away the burnt bit? I had to do it once and it was fine. Sorry if that's no use.
I've used barb's suggestion quite successfully. If it's quite bad I have also heard of scraping off some pile from another area of the carpet (say from under a sofa) and glueing it over the mark
try careful brushing the burnt area with a wire brush (one of those brass ones that you get in a cheap set of 3). This will remove the burnt bit and fluff up the pile so that the hole isn't so noticeable. when it doesn't work try the previous suggestions.