Unresponsive Trackpad Click After Battery Depletion
Usually OS X machines will go to sleep when they run low on battery.

The fact that yours didn't suggests a battery fault.

I used to be a technician and I saw clicking affected when the battery swells (as the battery sits directly on top of the trackpad assembly).

Does the click feel normal (still get the normal click noise when you press the trackpad)? If not, I would suggest taking it in to be looked at by a technician.