Thar "small round part" is the outer end of the pitch motor's shaft. If I recall correctly what you can see in your photo is a metal cover that goes over the metal pieces that alternately get pushed then pulled by the magnetic fields of the electro-magnets that are affixed to the black circular disk right next to it. I've seen these covers come off before - they are pretty much just a tight press fit. You should be able to push it on and it should stay in place. Just make sure you line it up with any visible match-marks, orientation keys, or other visible aids.
When you try to pitch the camera up or down by using the pitch wheel on your RC, do you hear a clicking sound coming from that motor (but the camera does not move, or moves with short, jerky motions? If so, the fix is relatively easy - the motor shaft has rotated out of it's proper position in relation to a pick-up sensor on the circuit board. It can be re-oriented back to it's proper position easily.