Stop thinking they are worse than you if you keep losing to them. Relax, keep the ball in play, and start winning, and then you will be the better player. You may be trying to hard to finish points. Just outrally this guy if you have troubles finishing. Let him make the mistake of going for too much.
You have to find a way to play loose. I had this same problem a long time ago. I lost to a guy probably 3 or 4 times even though I was better than him, because I just put too much pressure on myself. The next time i was suppose to play him, I broke a string and had to borrow a racquet from someone else. With this built in excuse, I played loose and beat him easily. Even though we played many times over the next two years he never beat me again. I think learning to play loose is something that comes with experience. Good Luck!!!
A couple of things, first, if people beat you they are better than you, by definition. Second, there is a complete difference between great strokes and great tennis. The latter requires a solid Mental Game, which just hitting does not. You need to become match tough. Play more matches and work on your composure.