Aaron was ashamed [and was reluctant to assume the position of High Priest] because of his role in the Golden Calf episode, and Moses said, "This is why you were selected" (Rashi, Leviticus 9:7).
I was once asked to see a student nurse who was beside herself because she had made an error in medication. While this particular error was harmless, she felt that she lacked the competency to be a nurse, because she saw that she was capable of making even more serious errors.
I told the young woman that I did not know of anyone who can go through life without making any errors. Perfection belongs to God alone. If all nurses who became so upset because of a medication error would leave the field, the only ones who would remain would be those indifferent to making errors, and that would be the worst disservice to mankind.
We must try to do our very best at everything we do, particularly when it concerns others' welfare. We must not be lax, negligent, nor reckless. We should of course be reasonably upset upon making a mistake and learn from such experiences how we might avoid repeating them. However, if in spite of our best efforts we commit errors as a result of our human fallibility, we should not give up. Allowing a mistake to totally shatter us would result in our not doing anything in order to avoid mistakes. This non-action would constitute the greatest mistake of all.