First, how big is the opening for inserting the drawstring? How big is the overall casing? Are you using a drawstring tool or a safety pin? What size? Make sure both the tool and the drawstring are not too big for the opening!
The twisted cords knot well and are a good all-purpose cord, but the ends will really fray and the cord will untwist.
Oh, and what do I use to insert the drawstring? I use a bodkin. I like to joke that you shouldn't work at a fabric store if you don't know what a bodkin is!