I suspect that your real motive for posting here was that you were salty about getting drawn out on and want us to join you in berating your opponent’s play. If you really are interested in how to play the spot he’s in, put yourself on a shoving range. What hands could you have in this spot? Then look at how much equity AJ has against those hands and compare them to the pot odds Villain is getting. 

“Chip preservation” isn’t really a useful way of thinking. It’s always good to avoid losing chips. It’s always good to win chips. Equity and pot odds is a way of quantifying and comparing these two things to each other so that we can decide which play will give us the most chips, on average.

Everything is math and ranges. If you call with a hand that does not have enough equity to call, then you got outplayed. If you fold when you did have enough equity to call, then you got outplayed. In this case, you got your opponent to call your shove with a hand that was well behind yours. You outplayed him, and he got lucky.

If you’re worried about getting outplayed in a certain spot, ask yourself: “If my opponent knew that I were going to fold this hand, how could he exploit that information?” Generally the answer is that he could bet more often as a bluff, because he has more fold equity. So the question then becomes whether there are enough other hands you could have that would continue to a bet such that even if you are folding this one, bluffing still is not profitable for your opponent. 

I think it would be more helpful for you to post a hand where you folded and worried that it was a bad fold, rather than one where your opponent called but you don’t think you would have. Among other things, it’s possible that you wouldn’t end up in this spot in the first place because you wouldn’t (I hope) have made that tiny out of position 3bet.

In my experience, when people worry that their opponents are making hugely exploitive plays against them, it is mostly in their heads. Many of your opponents are just playing their own cards and not thinking much about you or how you play. Many do not use HUDs. Many wouldn’t know how to take advantage of that information even if they had it. Don’t worry so much about what your opponents are doing and whether or not is correct, and certainly don’t assume that just because they won the pot they must have played correctly. Most of them, even if they are slightly better than you are right now, are overall quite bad at poker and not people you should be trying to learn from.