First off, when practicing for yourself, SLOW DOWN enough in the beginning that you can't make mistakes. If later you have a piece up to speed and develop a new habitual mistake, SLOW DOWN and practice that passage (not just the measure) over again slowly enough to play it correctly. One learns mistakes exactly in the same way one learns correct movements, by repetition, and it is important to spend all your practice time learning the correct movements, not the wrong ones.
Later, find a gig where the audience doesn't care, and play for them. I played for a junior choir in a church for years, and as they got better I got a lot better. Even though my favorite repretoire was the Stamps-Baxter chestnuts that were "repurposed" decades ago by the Barney PBS show for general happiness training, nobody objected I was teaching these pieces for their original Christian purpose. Look around, most junior choirs these days are using CD's and kareoke machines, and a little live music can cut back the glitz and dance and focus the kids more on learning the words and concepts.
Lately, I've been playing for the Saturday free to all who come dinner, at a church downtown. Nobody else plays for them when I am not there, and they hardly notice. But I was gratified when before Christmas, in the midst of all the high class Christmas music I was playing (Holly & the Ivy arr. Winston, In the Bleak Midwinter hymn etc), some old indigent started pounding the table in rhythm to Jingle Bells. At least I touched one person emotionally last year, even though it wasn't my favorite piece.
So, perform, get over the nerves, not everybody is as discriminating as you are, and you'll never please professional critics anyway, don't bother. Real life is not like school, and everybody can find something nasty to say. Challenge critics by coming right back with "All right, you're so good, play something for me that you can do better! Right NOW!"