Concentration is an important thing to have, when you are performing. Don't let your mind wander. After that, it is a case of knowing your pieces really well. You need to analyse your pieces and understand them on a theoretical level, as well as breaking them down at the piano and developing the ability to start anywhere in the piece. Knowing as much as you possibly can about the piece will give your mind more than enough to fall back on, if it makes a mistake.
But possibly even more important - don't make mistakes in your practise. It is easier than you think to 'learn' something, and playing a passage wrong two or three times can leave your subconscious with a dilemma in performance. Does it go with the correct version or does it go with the wrong version and run straight into a blind alley, so to speak? You say that you have mistakes occurring anywhere in your piece - well I'd bet good money that they occur where you once had mistakes in your practice. Make a note of any mistakes you ever make, and once you have finished your run-through, go back and work on those areas. Ingrain the correct way to play the piece and remain aware of what could go wrong when you play through. Finally, develop strategies which will enable you to carry on if there areas do go wrong again.
You're not going to get all that into your playing overnight, but in time you can learn good performance strategies.
Richard.