You haven't explained this very well. Did you just open jam the flop when you missed? Typically, you'll be getting around 3-1 to call here and A3s flops perfectly well with those
odds. If you had more chips and thus more fold
equity, a shove may well be better but since the opener is likely calling with most of his opening range with your stack, a flat is fine and then you can just check/shove any time you flop a FD, SD, TP, two pair or trips profitably as well as board like 255 w/ one of your suit where you have a gutshot, an over and a backdoor flush draw. This board is not the kind of board where you would want to shove since when you're called you usually have at best 3 outs and are hardly ever ahead.
You also seem to have a fundemental flaw in your thinking. If a hand flops well, it is better to flat with here since you will hit enough boards that you can get it in on. If it doesn't flop well but has decent equity versus villain's opening range (like A7o or 44, for example), these would be a better candidate for shoving.