She probably should have introduced you. That would have been the best thing to do. I don’t think she meant to slight you, though.
In this day and age, people 55 years and under (this is a generalization based on my own experience) don’t know how to do introductions and don’t know why they are important.
Your girlfriend probably assumed, or remembered incorrectly, that all of these people already knew you (because she probably talks about you to them) but forgot the fact that you have never actually met any of them, even though she has probably mentioned some or all of their names to you. Then, because it was her birthday and things were moving pretty fast, she probably didn’t even think to introduce you. At that point, you probably should have introduced yourself.
However, even if you introduced yourself, that might not have remedied the situation. I would say, that over the last 2 years, half of the people that I was meeting for the first time, were not introduced to me by the person I was with. So I said to the new person, “Hi, my name is Kardamom, I work with Rex here.” The response was either, “Oh” or “Hi” to which I then had to ask, “And what is your name?” No one seemed to be put off by the fact that I had to both introduce myself, and then try to ascertain who they were.
When I was in elementary school in the early 1970’s we were taught how to make introductions and then we practiced doing them when our parents came to our open house nights. We were expected to know how to do that. I don’t think most people, including those of my own age group (50’s and over) know how to do it.
I also know that when people get to a certain age, this usually starts in the late 30’s, that you tend to forget names, even of people that you have known for years. Even people that you work with every single day. When faced with introducing a new person to a crowd of people, it can be very embarrassing if you forget the name of someone who shares an office with you, or one of your old schoolmates. So, from this point on, I have decided that I will introduce myself and try not to make a big scene out of it. I also know, that I am also going to have to ask the other person who they are, because they likely aren’t going to introduce themselves to me.
In the meantime, you probably should very gently say something to her, now that it’s after the fact, so that in the future, she’ll remember that she needs to introduce you. Be very gentle and use a bit of humor when you bring this up. Say something like, “You know Karen, at your birthday party, you forgot to introduce me to your friends. I know that you know them, but I had never met any of them. Did you forget that I had never met any of them? I kind of felt like odd man out.” That ought to get the point across without offending her. If it does happen to offend her, then you’ve got a problem you didn’t know you had.
Next question: How do we bring back teaching proper introductions in elementary school?