If something is able to come out accidentally/so easily like that, it likely isn't meant to have too significant of a role in the seal of the bottle. I would believe the rubber does the actual airtight seal and then the metal is there mainly to keep the rubber securely in place. I would believe that the plastic that came off on your bottle is there to allow access to the rubber (if it revealed the rubber), to take a sample of the Nembutal through it with a syringe without otherwise disrupting the seal.
If it helps to ease your mind further, you could wrap the bottle with plastic food wrap to be totally sure no air will be coming through, but in all likeliness there is no need for this. I really believe you have nothing to worry about here and I wouldn't lose sleep over this. :)