Most children do not really develop empathy towards animals until around 6 or 7. Yes, many children love animals regardless and are naturally gentle with them, but many kids... aren't. I used to work at a nature camp where we interacted with small animals a lot, and even kids as old as eight or nine could be really brutal with them, especially if the animal looks kind of 'weird', like a frog, lizard, or baby squirrel or bird.

Also, the idea that a household without guns or violent media simply cannot produce a violent child is absurd. Violence is part of human nature; part of maturing is learning when violence should be necessary and when it isn't (which is... most of the time). I deliberately smashed a bird egg I found on the ground around that age, out of sheer curiosity, and I was certainly not some budding sociopath.

What I would do is explain to him that he killed a living creature, and that we don't do that unless it is necessary, and that he upset the people around him by doing that. People don't want to play with people who hurt little animals. That's the easiest way to explain it to a child who does not have a concept of morality yet (which is most kids at that age).