Celluloid can fall apart into crystalized pieces but it's unlikely your washing caused that. Certain glues used in assembling celluloid buttons long ago often caused ruin of the button many years later. Storage for long periods with other materials can also cause celluloids to crystallize and fall apart. Here are some images of celluloid buttons which are well on their way to ruin:

The one-hole items are probably beads although some buttons had a metal wire through the center,looped in the back for a shank, those are called "pin-shank" buttons, if the pin shank came out, a disk with one hole in the center would be left. You can tell if the left over one-hole piece is button shaped or more like a bead. -Carol-