You can tell by the voltage. LiPo batteries have a distinct "knee" in their performance, generally around 3.4V-3.6V:
It will be slightly different depending on the exact battery, and how you've arranged them in your battery packs (you need to account for the current load when measuring the voltage) -- so it makes sense to characterize your own battery first.
Since your batteries will be in a quadcopter, the best solution will depend on whether you favor the safety of the battery (immediate hardware shutoff) or the safety of the platform (warn the autonomy, allow it to land safely before it shuts itself down in software).