I agree that you need to be careful on how you point out mistakes. I realize this was the teacher and there's not much you can do about the way someone else says things to your daughter. At home, however, practice "sandwiching" mistakes with compliments (compliment something, point out error, compliment something else). I always had to reassure my children that mistakes is how we grow and learn. If we never made mistakes, then we would already know everything and there would be no growth. Since people continue to learn and grow throughout their lives, that means that people will make mistakes throughout their lives. What gets them through is the knowledge that they did their best and that's all you can do.
Some kids are perfectionists for whatever reason. My oldest daughter has ALWAYS been extremely hard on herself for making mistakes. She is 21 now and I still find myself needing to reassure her that she has done her best and that's all that matters. She's not 5 anymore so she doesn't burst out crying, but she completely stresses out. This drive has helped her in college (her GPA is 3.85), but it sure does make it stressful for her. My other daughter is completely opposite. She does her best and that's all she can do. She is completely fine with it. She also does very well in college, but is much more relaxed overall. My oldest son was also a perfectionist and refused to accept responsibility for anything he ever did wrong (had the blame game all figured out). He finally mellowed out and started owning up to things when he hit his teens (I actually have enjoyed his teen years MUCH better than the early years). I have other boys who aren't so hard on themselves. My point is that many times it is the child's personality and not something you did, so the only thing you can do is to coach your daughter in overcoming destructive thought processes (I'm wrong = I'm bad for example). Just do your best to continue to encourage her and reinforce what is good. Find things to compliment her on and make a point to mention to her how good she is at those things. As she hears more positives than negatives, she will overcome her sensitivity. Just be aware that some kids hear negatives a lot louder than the positives, so it makes it even more challenging.