I'm playing with semantics a bit (for which I apologise) but I'd prefer to call it self assessment. We've all self-criticised - come off stage thinking we've had a bit of a 'mare, only for others to tell us we played well - and while it can be a driver to improve, it can also be a bit unhelpful. It's fine to say "I didn't play very well" but that won't help you improve unless you can say "I didn't play well because ....." . I've also found that most bands have at least one "drama queen" who will denigrate their own performances, particularly at contests, virtually every time they play. This sort of self-criticism is, imho, not only unhelpful, but becomes a kind of self-fulfilling prophecy where the player starts believing that they are in fact worse than they are. They then expect to perform badly, fulfill their expectations and continue the cycle by telling everyone how badly they played - resulting in the self confidence issues that Gordon mentioned.
In other words, I feel "self-criticism" in itself cannot promote better playing (or improvement in any area of life), but good "self-assessment" can. I feel it is much more useful if you don't just criticise yourself, but assess (as objectively as you can) how you performed, which areas could be improved, which areas are in need of most improvement and which areas you can improve on your own without outside help (by the sound of it this is what Stephen is doing on a regular basis). Then if there are things which can only be improved by getting outside help - in the case of brass playing, by getting a few lessons with a good teacher - you can decide for yourself whether the improvement you want to make is worth the investment of time and money.
I've often found that the difference between two naturally talented people in any field is the ability to accurately and objectively assess their own performance.