present in the soil. let the soil get a little dry on the surface before watering. don't plant the basil in too large a pot for the size of the plant. only size the pot up, when the plant is so large that it may be getting pot bound. that way you will not have too much soil for the amount of roots and are less likely to over water, or for the soil to stay overly moist for too long a period.
it's hard to tell what went wrong, but i am guessing perhaps temperature. for now would buy starts and you can start some from seed. check the thread 