Obviously, this was a rude, thoughtless, disrespectful thing to do. I agree with another poster that the birthday girl's mother really should be held responsible.
I agree with the teacher who said not to sugarcoat this with your daughter. Even if this not a child your daughter would invite to her party, even if they are not particularly close, it hurts to be the only child excluded.
Coaching your daughter on appropriate responses aside, this hurts. Validate your daughter's feelings and bring this to the attention of the teacher. While the teacher cannot police every behavior in her class, she would probably like to be aware of this circumstance and she certainly can reinforce expectated behavior and remind students of the importance of being respectful to others.
I also disagree with alot of the moms here who think it is ok to use the teacher to distribute party invitations. Unless it is a school sponsored event then invitations should be mailed or personal phone calls should be made. If you don't know the invitees to your child's birthday party well enough to find a way to contact them outside of school, maybe they don't belong at your child's birthday party.