There are some slightly unusual features here that need to be sorted out correctly. First, the upper valve (exhaust valve) has a steel pushrod, with a painted red band around it, while the lower valve (intake valve) has an aluminium pushrod. You need to make sure they are in their correct places.
Second, the small round bit that fell off the top of the valve, shouldn't have been able to do that. It is supposed to be held in place by the rocker arm, which in turn is located by the pushrod. I don't see how it could come off unless the engine had an enormous exhaust valve clearance (which would make it clack horribly when it ran, like a vintage removal van), or the round bit is damaged, or perhaps if the valve retainer is failing and moving up the valve stem. (A less likely possible cause would be if the engine were overspeeded, resulting in valve-bounce, but that shouldn't happen on a governed engine unless someone intervened.) I think you need to remove the other (inlet) rocker and examine its little round bit for comparison with the one that fell off. I don't think you should reassemble the valve gear until the failure has been explained.
