You do just need to laugh it off, and generally take things less to heart - a date is just a date.
There's nothing wrong with sleeping with someone on a first date, you don't need to be self conscious about it. There's nothing much wrong with drinking too much, most people do it some time, you don't need to berate yourself.
Who knows why he didn't come back - most likely just because while he had a good time with you, he just didn't think there was a future in it. No one likes rejection, but dating is numbers game, you won't click with the vast majority of people.
However, if your behaviour did put him off - it will be because you were apologising for yourself and making a big deal of getting drunk and shagging. Being embarrassed because you slept with him is obviously not very flattering to him, plus the fact no one likes people who endlessly apologise and go on about things in general.
You do sound very young OP - more like 22 than 34. If you have a real problem with anxiety and can't get out of it on your own, then go see your GP and investigate CBT because it sounds like it might be messing up your life a bit.
Other than that, the only to do is get back out dating - and remember that a date is just a date, a few hours in a very long life.