Ah! Welcome to the world of 'ping' and the Carpet Monster! Believe me, it won't be the last time that happens, especially with tweezers. Depending on the shape of the part,and at what angle you have to twist your wrist to attach it (!), sometimes 'reverse action' tweezers can help. These have a small spring inside, keeping the tweezers closed until squeezed to open them , the opposite to 'standard' tweezers. Personally, I find them a little difficult to manipulate, due to this stupid arthritis thing, so I tend to use very small pliers instead, where possible. A little tip for cutting and/or picking up small parts, particularly those you feel might go 'ping' - place the tip of a finger gently over the part before cutting/moving/picking up, to steady it, and stop it from 'pinging', especially as the knife blade makes the final separation, as this is where inertia rules!
As for the Carpet Monster, well, carpets were the desire and creation of women, so we're already losers! It's a fact that, once finished with a part, after perhaps hours of preparation and painting, said part will, upon being moved, and at the last second, disappear into the furthest reaches of the darkest, most inaccessible, dustiest part of the thickest carpet pile in the room, or perhaps even the next room, if the inertia of the 'ping' was strong enough!
First thing to do, if noticed in time, is try to listen for the soft noise it might make upon landing. Second thing, do not move your feet until you have scoured the area around you visually - the law of Murphy states that you will surely stand on, and crush the part, if you move first! Having satisfied yourself that it is safe to move your feet/chair/beer bottle/coffee mug etc, then do a 'square search' of the areas immediately around you, working outwards. This can be to a quite sizeable area, as the small parts seem to have powers the equivalent to a flea on extra -strong Valium!
If all else fails, and if physically able to, then lie flat on the floor, and look across the carpet at floor level, with your eye as close asd possible to the surface. Hopefully, the part will show up as a different shape, or tone or shadow against the carpet's surface. A bright lamp or torch sometimes helps, and placing a piece of plastic, or other material, of a similar colour can also help to identify the difference in tone to the carpet, and how the missing part(s) may appear against the surface of the pile. Of course, it must be remembered that, once all hope is lost, and a new part has been obtained or scratch-built, and the model is totally finished, then the missing part will turn up, normally in the most unexpected place!