It is generally thought that drunk people do not know what they are doing and they have no recollection of the things they do. Even though this is somewhat true, a more recent bit of research is making its way through the media that says drunk people do know what they are doing but just don't care. Researchers in 2012 apparently did a test where some people received alcohol and others did not.
Then, once the people had consumed the beverages, they were given tasks and subsequently asked to report on errors they may have made during the test. It turns out the drunk individuals were just as capable of reporting their errors as the non-drunk people, but those who had the alcohol didn't care as much about the mistakes made during the test.
This means the regret people may feel the day after getting drunk is real, but it is only caused by people not caring (at the time) what they are doing rather than finding out for the first time what they did.
As one of the researchers puts it, alcohol just shuts off the "alarm signal" that would normally tell people to stop doing something.