Your child's teacher sounds like she tells it like it is. That is, your child does not do work that is as neat as it should be. Maybe she knows your child can do much better work, like the kind you see at home. This may be a case where the teacher could be gentler with her comments to your sensitive child. Meet with the teacher and tell her how much you appreciate the high expectations, but also tell her of your concerns.
At the same time, ask the teacher for suggestions to improve neatness. Some helpful ideas to try: Verify that she is correctly forming letters. Make sure she is using appropriate spacing between letters, that the letters sit on the lines, and that they are of the correct size. You can do this at home as she does some writing for you or some homework.
This is an area where early habits need to be correct because they are very difficult to change. Kudos to you for jumping right in and supporting your daughter.