Is the stain darker than the carpet or did it bleach it and so the spot is lighter? If darker, it is quite possible a professional could get it out.
I don't know if you will have to pay for the damage, but I'll bet you won't, by the time you vacate.
Rearrange the furniture and cover it so you don't have to see it! Not the greatest idea but then at least you won't have to see it all the time