Get a very small drill bit and use your drill or dremmel to drill into the center of the stuck piece. If you slow your drill down as you're doing it, it will likely actually get stuck into the little piece. Pull it out with that. That would be my first choice.

Second choice, if that doesn't work, is to do the same, but after you get the tiny hole drilled, put a drop of super glue in it, put the drill bit back in, and let it set.