What if we turned this around? What if your mistakes where not mistakes but intentional "decorations" which propel you to go forward with your improvisation?
Remember this rule: if you repeat your "mistake" several times, it becomes intentional and they are no longer mistakes.
In this video (where I improvised a suite of 6 pieces for the group of French tourists) there are a number of "mistakes" which became intentional part of the piece. I "disguised" them by repeating an excerpt of the melody, or a chord progression or a rhythm which didn't seem to work well at first.
As you watch this video, pay attention especially at what's happening around 18:05, 20:17, 31:00 and you will see that these mistakes can be incorporated into the piece. Some people will not even notice them.
Try this trick today when you sit down on the organ bench and play for 10 minutes without resting.