A "lost head" nail is commonly called a jolt head (or bullet head nail).
See pic in case you aren't sure what I mean.
You bang it in, and if you want it lower than the surface you are nailing into, you just use a punch. If the surface is quite hard (like bare particleboard or something) you can actually punch it a little just by making your final hit with the hammer firm (and square on) enough.
In this case, you need to go below the level of the carpet, and of course you'd want it at least flush with the flooring underneath the carpet, so a punch is definitely needed.
See pic in case you aren't sure what I mean.
You bang it in, and if you want it lower than the surface you are nailing into, you just use a punch. If the surface is quite hard (like bare particleboard or something) you can actually punch it a little just by making your final hit with the hammer firm (and square on) enough.
In this case, you need to go below the level of the carpet, and of course you'd want it at least flush with the flooring underneath the carpet, so a punch is definitely needed.