You're totally not off base.
Like most sports/games/etcs.. Nothing is ever "won" per se, especially at the amateur level as the skill level is not good enough. You lose or your opponent loses.
The loser is the one that makes the last mistake. That's what I heard Kasparov say once anyway. He always reviewed his games, win/lose or draw. It's all about minimizing mistakes at every stage. A key thing is to recognize when your opponent has made a mistake, whether tactical or positional, and capitalize. Even still, very few players have the technique to convert an advantage without making mistakes themselves!
There is no such thing as an "I almost won except for some blunder in the end". You just made the last mistake, and it ended up costing you.