That's exactly what it is like Full3R... Heavy blunt trauma to the head (as in this case) is an exceptionally efficient and very humane way to kill something, especially if it is small. It feels absolutely nothing. It just sits there and then it is lights out. Once it is dead, why waste the body? Recycling is great.
Ash's dreams has got it wrong because she thinks smashing its head in isn't humane. It may be gross and harsh but it is very humane. You cannot argue with that.
In fact gassing it would have been worse for it, because it is like drowning in air. The animal can't breathe and panics then passes out.. It isn't exactly drifitng off for a nap.
Good on you Alex for doing the right thing.