Yeah, I remember wishing the guy/girl had played on...though, I had him/her in a bind, I still had no clue how to bring the game to a checkmating end. Would have preferred to see it play out....plus, I make lots of blunders in the endgame.
Does your opponent's rating make you play differently?

Feelings makes you play badly. Try not to think about such things, but focus instead
I absolutely agree with you. I think the problem is how to do that?
There are other psychological problems too; like losing an edge, but still having an ok position can be hard to adjust to. Or simply getting bored and playing a poor move, or trying to 'punish' an opponent for a move that wasn't that bad. These are all problems I think many players have, but there is very little discussion of them in chess books. I don't think it's just average players who have these problems, it seems to happen to masters too.

"I think the problem is how to do that?"
You can take specialized vitamins and cook up your own tea to help. For tea I'd recommend ginseng and white tea mixed while for vitamins Focus Factor is great. Just take a regular b-vitamin (as long as it has b6) if you think it's too expensive. I like Focus Factor for studying so I retain more information.

I see it as the pressure is more on the higher-rated player to win. The lower-rated player should not fear as "a loss is expected" but see it as an oppurtunity to make their opponent prove it. And steal some rating points in the process. As was said before, play the board, not the player. Early on (when I was Class C a long time ago in a galaxy far, far away...) I played hyper-aggressive against higher-rated players. Of course, more often than not, I got blown off the board but at least I got them to sweat a little bit. Lower-rated should see higher-rateds as prey for points, not the other way around.
That's happened to me before...someone overestimating me and resigning way too soon.