I used nylon inserts from the local hardware store.
How did you hold them when tightening the screws? Do you have long skinny arms with two or more elbows each? Kinda hard to reach nuts on the inside of the door after the panel is in place, isn't it? [on edit] OH, you mean the nylon license plate nuts that clip into a square hole.
The Rivnuts that Sack linked to would work. Also available from McMaster Carr (my hardware go-to).