MATE MATE MATE. First rule of PU DHV. You make it seem as if you are very needy there!! To be honest I'm not too sure how to repair the situation. I would actually not go for the whole 'I was drunk' angle because it makes no difference and it makes you look a bit of a coward and it will still be there in her mind AWKWARD to say the least.
I think the best way to go about it would be to not make any excuses at all and make it seem very sincere. If she says 'but you were drunk right?' say that you meant everything in the message and make her make the next move. Then there are three ways it will go:
1. She will see the message and know you mean it. Then if she doesn't want a relationship she will either ignore you forever.
2. If she values you as a friend but not BF material then she might just forget it ever happened and you guys still be friends but maybe it might escalate in the future to more.
3. Or she might like you as much as you like her and want to be your GF YAY !!!!!!!
Either way text her back like nothing ever happened and that you had a good night. Ignore her for a bit but in a few days/week time try and arrange a catch up in an informal way. If she blows you off then you know how she feels(1) and if not then the topic will probably come up and you guys can resolve it.(2+3).
Hope this is useful advice, you must feel like shit tho pal?? x