I think it's a bit excessive to suggest that after one such incident the child needs counseling or is a potential future serial killer. On the other hand, I don't get why some here are objecting to the suggestion that the OP find another home for the cat, at least temporarily.
For one, it seems that the child is not fully comprehending the consequences of his actions. That's really not weird for a three year old at all, and given time and proper direction that's something he'll most likely learn. In the meantime, however, it's really not fair to the cat to leave him in the path of potential harm just because you know your son didn't really understand what he was doing, and wouldn't have done it if he had understood. That isn't protecting either the cat or the child. The child needs time and the right environment to learn this lesson in a way that his healthy for him, and not harmful to anyone or anything else. If you really worry that he might physically harm the cat again, then the cat doesn't belong in your child's environment. (I'm not saying get rid of the cat, just ask a friend to keep him for a while until you feel the two are going to be safe together again.)
For two, there's a real possibility that the cat has connected his pain and fear with your son. If he feels threatened by your son in the future, he may well not be as gentle. If the cat lashes back when he feels unsafe, it might be a really vivid lesson in consequences for your son, but it probably won't be a good one. You want your son to learn empathy for the cat, not learn to see the cat as a danger or something he fights with. Now, you did say that your cat is unusually gentle... I suppose all my point is is that in my experience even the most gentle animal will get very nasty if they're truly afraid, and a sixteen pound cat can cause waaay more damage than you might imagine.
In the end, only you know what the risk is of your son doing something like this again is, so I don't know how much value any of our opinions really have. But you're a parent, and your duty is to put your child's development and welfare above any of your other concerns (guilt over punishing him when you think he didn't mean it, fear of losing your beloved cat, etc). It would be great if you could do that while still protecting the cat, because it depends on you quite a bit too. Good luck with that, and I'm sure your concern alone will help your son learn this important lesson.