@OP
The reason why you didn't play fxg3 is that you do not understand why it is better than hxg3.
Sure, engine here takes with the queen and you get material advantage, so it is clear, but human wouldn't play it that way, unless he/she too understands why they should do it.
The reason why fxg3 is better is not straightforward - well certainly not like you showed. I understand it, sort of, but the thing is that you don't get some material advantage immediately.
First of all, fxg3 is not really intuitive because the opponent gets a tempo move with check. But more importantly white gains a half open file and the access to f6 square that is not defended with a pawn, all the while black's king is weak.
So because white is winning, black (engine) understands this and gives up a queen. Why is white winning? Because black's king is weak and if white manages to put a piece on f6 in addition with Qh5, he will create a lot of threats around black king, and eventually if followed up correctly, white will be winning.
So unless you saw that during the game, you didn't know fxg is better, and let me tell you this, there is a chance that I wouldn't see it (during a really long game, say 1 hour per side), and probably some higher rated people than myself would have a chance of missing this as well.
Many lower rated players probably wouldn't understand why fxg is better even during analysis.
In essence, you need to become a better player and you will miss less.
When you analyze your games, don't always follow engine recommendations. You should sometimes, but when you see something you wouldn't do (for instance you wouldn't really want to give up a queen if you were black), try a different response, and see why it is worse than the engine recommendation (giving up a queen in this case). You can learn a lot like that, and you will understand more going forward.
I saw the move and the reasoning behind it. I was just not sure about myself so I didn`t play it. I knew for a fact that is better but was not able to bring myself together and play it. It is different problem that what you described
You don't play it because you find the moves based purely on intuition but don't back it up with concrete variations and ideas. You don't understand why the move you thought about is the best and that's the problem. Never try to imitate the engine, use human logic and play like a human. Engines don't use any logic they Just calculate.