Little girls... often find older girls very enchanting and interesting. And they get infatuated with them sometimes.
I have a daughter.
But, its just one of those things, that the younger girl has to deal with... that is life. They can't have their playmate/friend to play with all the time and when they want. It is not instant. And older girls have interests/development that is not in line with their own development and their own lives, and they have a Mommy too.
A child just has to learn, even if it is disappointing or frustrating, that everyone is busy or has a life and their own family. But at 4 years old they don't have total impulse control nor over their feelings.
Its okay to be excited, but learning "patience" is hard for them.
But its life.
And also, hopefully the older girl does not start to feel "pressured" about having to play with your 4 year old. Because then that will be stressful. For her. And/or, what if the older girl starts to avoid, your daughter? Because she feels too pressured to play with her?
And, certainly I would hope that the older girl does not feel put on about, for being "responsible" for your daughter's happiness or not.
But it is things like this, that a 4 year old needs to learn what is rude or acceptable... upon other people. But they are so young... that it is hard for them to know that.
Does your daughter have other friends or playmates?
With my daughter I would just explain to her that everyone is busy, and the older (in her case the daughter of a family friend) girl is busy and she is OLDER than her, so her interests are different than hers. And in some cases, Teenager interests are not age appropriate or compatible with hers. My daughter would understand that.
It is a life lesson.
Or maybe, she is ready for Preschool? 4 is when my son started Preschool and was ready. He needed the extra interaction and enjoyed it.