Don't send that message.
Perhaps it was a numbers thing, perhaps she was forgotten, perhaps the little girl didn't want your daughter at the party or maybe this particular one for her own personal reasons. Children have feelings and emotions too..they also know who they want to hang around and don't.
Maybe the parents tried to convince their daughter to invite yours, but the little girl was adamant about not inviting her.
Don't send a letter or anything. That is being petty, showing desperation, not being respectful. Don't hold a grudge against the child or parents.. don't stop inviting their daughter, unless there is conflict among the parents, harmful to your daughters well being, or only if your daughter decides not to invite her.
It's tough, but unfortunately it is a life lesson that your daughter needed to learn at some point in life.
Hopefully this doesn't have a lifelong impact and impression on your daughter. Hopefully at 30, she won't be telling of the way this traumatized her.
I suggest you have a sit down with her and explain that she won't be invited to everything, and that it's okay not to be.
Perhaps you can plan a special day for her, if she had 1 available friend, perhaps invite them over.
This breaks my heart..but it is a life lesson we all learn eventually.