Its not supposed to come in contact with the diapers. Most true diaper pails have stots on the underside of the lid to slide the disk into.
If yours doest try taking a small container. (yogurt, cream cheese, small butter ect) hot glue the lid of the container under the lid of your pail and punch a bunch of holes in the bowl part. Now put your disk into the bowl and snap it into the lid.
Did that make any since at all????