Your photo motivated me to check my door latch post before I finished my morning coffee!! My latch post wasn't loose, but it wasn't tight either. Thanks!!
I have not worked on my door, but I have removed the door interior trim, inside handle, headache pad, and interior sheet aluminum rivets to access wiring inside the wall next to the door. Removing these parts is straight forward screw-and-rivet removal.
The door frame is tight to the end wall rib. Removing the interior pieces mentioned may allow you to retrieve your part. If you can't get the part out you may have to remove the door frame.
Also, the threaded part that fell was probably secured with rivets or screws to either the end wall rib or door frame. Perhaps you can see the means of attachment thru the hole the latch post occupied.
Good luck! Let us know how you solved the problem.
"To err is human, to air is devine."