For fuck's sake, I have never known so many moany ranty people on one thread before.
So the OP called the (miserable) teacher an older lady! So what?! If the OP is youngish (like 30, am guessing,) 50 IS older. FFS, people do love to moan, don't they?! 
And now calling women LADIES is a fucking insult? Jeeeeeeez!
OP, all you need say to your poor little daughter is 'the teacher was having a bad day and was in a grumpy mood. Like the grinch or scrooge she is grumpy sometimes.' Bless her little heart getting so upset! However, I guess she has to learn eventually that not everyone is nice all the time. Better that she learns it a bit older, but she does need to know that people can be shitty sometimes.
Thing is, she has you for a mother @whyisnothingeasy so she will be fine. 
Give her a hug and let her know most people are nice, most of the time, but sometimes people can be rude, and she should not take it personally. 
I remember my cousin's little girl going up to this woman and her partner when she and my cousin went for a summer walk. She handed this woman a handful of daisies and said 'pressie for you.' The woman (about 40,) said 'no thank you, I hate flowers!' and turned her back.
Thing is, some people are twats sometimes. It's a shame, but they are.
The teacher should not have been like this though. She is meant to like children isn't she? At least a bit! 