If it's just the plastic front cover piece that broke off then you can probably just clean up the mating surfaces with alcohol and secure the piece with epoxy or some other strong adhesive.
If that cover piece broke into several pieces or is otherwise not salvageable then you may have to buy a whole interior door panel. You may be able to get a used one from an auto recycler for a reasonable price. Here's one on eBay for $100 including shipping...