Most play better in practice than in competition. That is due to wrong thinking. And, we all are guilty of it at times. In reality, the only pressure there is, is the pressure that YOU put there. The simple answer is, if you play worse under pressure, then don't put that pressure on yourself!
Easier said than done?? Not really, it's as simple as just saying that you have no pressure. Just play, and see how it goes. We WANT to say "hey, this match is important, be real careful". But, in doing that, we are adding pressure that is counterproductive. So... don't do that. Instead, just get in the habit, even in practice, of doing each shot the "right way". Give each shot the attention it deserves, but no more. Just make the ball, and then put the cb "over here".
THAT is the correct way to play. Watch Rodney Morris some time. He looks like he's just practicing. Actually, he's just got a job to do, and is getting that job done. He's not standing there worrying about what someone else will say, or if he will miss, or anything else negative and counter productive. He is just doing what he is supposed to do.
You don't give a second thought when you take a drink while you are playing about what someone else is going to think about how you grab your glass and drink out of it, you just do it. Why then worry about what someone else thinks about how you grab your cue and stroke it?
Believe in yourself. Be your best friend, not your worse enemy.