I asked my girlfriend to shave her upper lip
Why would you ask her that?
I was disgusted by the sight of a furry upper lip
Telling her to shave her upper lip is pretty insulting behavior. Did you realize that she might be hurt by that? If it's really important to you, you should have brought it up in a nicer way.
She will learn to do it by herself.
It seems that what's done is done, but I think you should apologize to your girlfriend if you hurt her feelings. From there, it would be good to find gentler ways for her to remove hair than using a razor.