to be honest, the safest thing to ensure the threads don't come loose is the backstitch suggestion. but, if you want to take a chance, your only way to go is fabric glue.
shop carefully. look for glue that's made for fabrics. make sure it's made to NOT wash out. i'm at work, and don't remember the name, but they sell a very good one in the craft dept at walmart. it's clear and so is the bottle.