I was thinking about this the other day, the whole concept that if two straight people who are of opposite sexes really, really like each other, well, there must be some sexual component, no?
What about two straight women who are good friends? Two straight men?
A real connection can be there with absolutely no sexual attraction. It just means you LIKE each other. That can happen without sex, really. ;-)
Unfortunately, since you guys have already had sex, and she thinks it's a big deal, it's all more complicated. If it was before anything had happened, I'd say, great, you have a friend! Make sure you keep it that way, keep things clear, don't do anything to hurt her. It may be too late for that, but if you're very honest about how important she is to you, who knows, could still happen. I haven't managed to remain close friends with anyone I was in a romantic relationship with, but lots of people do. And this was so transitory -- twice? while drunk? -- that it can't even be called a romantic relationship, really.
Just lay it out there, see what happens. She may well prefer to keep your friendship, too.
I completely agree with Ceili, though, I don't think this is something you want to push further. A really good friend is a cool thing in and of itself, and the alternative could get way ugly.