One of the things that most throws us out of balance when playing in public is a heightened awareness of what is going on. You can, and should, prepare for this when you practice. Before you practice, close your eyes and take a few deep breaths. Hold the air in and then concentrate on the way your body relaxes as you breathe out. Now start to notice and label the different sounds you perceive, trying to listen to the most distant of these; other people talking outside of your practice room, cars passing a nearby street, the sound of your own breathing, the sound of the pipes in your house, etc. You will quickly notice how much more noisy it is when you start noticing all these things. Now be aware of how the seat feels beneath you, of the solidity of the ground, of the air around you, of the temperature. Now look around you and notice the appearance and position of objects in your room, the way your hands and the keyboard look.
Take a few minutes each day to settle into your practice environment, it will help you practice better. It will also prepare you for the heightened sensory awareness that is the result of the adrenaline rush that comes from the fear of public performance.