You're supposed to use a hook, insert it directly behind the handle (parallel with the handle) with the hook facing you, and you should be able to get ahold of it.

If you don't have something w/ a small hook on it laying around, I would try bending a coat hanger. You'll need to use a needle-nose pliers or something similar to bend it into a small enough hook to fit in that space.

A screwdriver might work, but I would think you'd have to jack up those surfaces a bit in the process. Might bend the clip a bit as well.