How is it possible for one to win by any way other than one's opponent "missing a key move"?
When you win due to an opponent missing a key move...

Just remember the old saying - The winner of a game is the person who made the next-to-the-last mistake.

All you can do is take comfort in the fact that you can clearly see more of what's actually happening on the board than the opponent did, albeit later than you would like.
When you realise you've screwed up it becomes so obvious that you can't believe the other guy missed it.
I know exactly what you mean, happens to me all the time lately. It leaves you questioning just how good you are at the game.
Deep down you know your good but find yourself secretly wondering if your fooling yourself. It can be frustrating, especially when you find yourself going through a losing streak.
I suppose that's how the game works. Past a certain level of skill you don't really play the opponent, you play yourself.
It's a Bruce Lee moment, when asked 'How do you see your opponent?'. Simply put, 'There is no opponent.'. Maybe that is the secret to Chess, cut the opponent out of the equation and just play the board.
Then all the pieces on the board become yours, to win the game for black or white you have to limit the abilities of the pieces you don't have complete control over.
Easy said.

Well, I was once in a seven-game losing streak, and I was truly at the worst of my chess ability at that time.
But sometimes, losses become a platform for you to improve. Now, I've not lost a game in 10+ games.
Well, of course, I still have games which are lost, but those are due to inaccuracies, and I really hope not, missing key moves.
Btw, woton, that's a quote that got me brain cells wondering.

The level of a player is dependent on executing better moves that gain pieces and/or win. there are many theories on what that actually is but that is not important to your topic.
In your case it just seems like you over analyzed the situation. You saw the move/s that could of defeated you and your opponent did not. if you proses your move a bit better you would of played more to your potential and still would of avoided the move that could of defeated you. in other words take your time.

I know. I've always thought it strange how so many people get pretty good at chess, then just vanish.

I take comfort in the fact that players at my level (and above) make mistakes and blunders quite often. I consider it a good game when I get less than 25% inaccuracies and mistakes. I won a hard fought game which I thought was well played...4 Blunders and 40% of moves were either !?, ? or ?? It's just that my opponent managed to play worse than me.
We all miss moves, usually without knowing it.
The experts say to review every game you play with a notepad in hand. Notate you feelings about the entire game, and any key moves or combinations. Sounds easy... wrong.
This exercise beat my ego up so badly my rating dropped over 150 points in a week. Sure I found some of my opponents missed moves, but I missed mates, had exposures to forks, pins, left pieces hung for a series of moves - while developing attacks that actually strengthened my opponents position. After the review I could not make moves in any of my games for fear that I was making some sort of blunder. But the fact is, they did not capitalize on many of the mistakes.
It is all what you see when you look at the board.
It is all what they see when they look at the board.
Nothing else matters.
I'm sure if you had of stuck with the method through the temporary loss of points you would have seen an improvement. The nature of long-term improvement in general is that it will come at the initial price of a few rating points. And of course the method doesn't work just on its own. You need to actually put in some hard study into the areas where after analysis you can see you are weakest in..