The two best methods I know of are very simple.
First, wear an apron and attach the bottom of it with clamps on both sides to your workbench.

Secondly, put a large piece of white plastic sheeting under your workbench so that it projects out a couple of feet in every direction. It is much easier to find fly away parts on the sheet of plastic.

attatch magnetic strip or velcro to the apron, much less dramatic than clamps if you stand up or turn absent mindedly

You can't actually defeat the carpet monster because it doesn't exist. In reality, the world is full of eddies in the time-space continuum, which, being ever so slightly more dense (at the quantum level) than the surrounding energy state, tend to naturally settle around the floor. These eddies actually constitute the free ends of wormholes in the time-space continuum, of which three types are known to exist.

The first is a wormhole to the present, and any piece falling into one of these simply re-appears immediately, but likely in a different 'where'; presumably halfway cross the room in an impossibly remote spot.

The second is a wormhole to the future. Any piece falling into it will typically turn up in a fairly predictable spot, but only after a considerable amount of time (and searching!) when the present is able to catch up to it.

The third is the most insidious,being a wormhole to the past. Any piece falling in one of those is never seen again.

I always thought of them as "gremlins".