Asked a girl out and got rejected, she's a main character in my social group. how do I "next" her?

I don't want to be rude but slowly withdraw from her. Didn't really lose anything but time and I have a lot of that in high school. Do I maintain friendship (basically friendzone) or just cut her off completely. I know the latter is preferred around here but she is in my social group and I don't want to come off as an asshole.