Alcohol encourages altered behavioral patterns. That's a fancy, Psych 101 way of saying that drunk people do things they normally wouldn't do. Among the many funny, strange and terrible things people do under the influence of alcohol, one of the stone classics is the drunk hook-up. Now, I personally believe it should qualify as some sort of physical feat to successfully consummate a relationship, no matter how brief, while affected by a depressant that just loves to inhibit motor function, but there are also major emotional ramifications in the aftermath. There is a right and wrong way to deal with the morning after drunk sex and I'm here to make some important suggestions in that regard.
First, let's get the most awkward topic out of the way. Sex between two drunk adults is no more rape than sex between two 16-year-olds is child molestation. If two people end up in bed together when they're in similar states of intoxication, they're in a mutual state of impaired consent. Because neither party was mentally competent at the time, neither is more or less to blame for how things ended up, assuming that both parties got drunk on their own accord. It's not a good way to hook up and it's nothing anyone, under any circumstances, should do intentionally, but it's also not the worst thing that could happen to a potential couple.
I know it may seem weird, but if you do end up in a morning after a drunk hook-up situation, it's probably best to embrace it. At some point shortly after waking, you two lushes need to have a frank discussion. Morning salutations and pleasantries are all well and good, but it's only fair to determine if the two of you tumbled into bed together just because your judgment was impaired or because you're actually attracted to one another. The test for this one is easy: Are you still at all interested now that the sauce is off your brains? If the answer is "yes" from both parties, do the counterintuitive thing and spend the day together, if at all possible.
Yes, I advise experiencing a hangover with your new potential partner. It's not going to be a pleasant experience, at least at first, but believe me, it's a gift. Hung-over people are disgusting, irritable and almost completely devoid of pretension. It's not likely that either of you will have the energy to put on airs for one another when you're battling a multi-system emergency condition throughout your bodies. Most relationships that last for any lengthy period of time take months to be as raw and honest as two hung-over people will be. If you still like this person after being with them at their most vile, you'll have fumbled your way into the building blocks of love.
On a more pleasant note, there's also a great deal of meaningful intimacy to be had in nursing one another through your respective hangovers. You'll learn some vital likes and dislikes, establish a foundation of tenderness and enjoy bonding through both commiseration and alternating instances of selflessness.
All this said, you both have a responsibility to give each other a proper, sober date following your little hangover experiment. This whole ordeal is a way to make the best of an ugly, embarrassing situation and it definitely shouldn't serve as a precedent for your relationship. The point of all of this is to re-frame the drunken hook-up as (potentially) not a mistake, but an opportunity. If there's any affection buried beneath your layers of hung-over agony, it'd be stupid to put it to waste just because of some common humiliation. Remember, it's not important how two people meet, just how they spend the rest of their time together.