The first question that needs addressing is whether you are just looking to avoid getting fired over this incident or whether you genuinely feel that you have a drinking problem.
If it's the former then don't go down that path, doing so would just be a dishonest attempt to weasel out of your current situation which is not only unethical (and disrespectful to those with genuine substance abuse problems) but would also likely become apparent to your employer that it's not genuine quite quickly and that could backfire massively! I think most companies would look more favorably on someone who made a genuine mistake and took responsibility for that mistake than someone who tried to make out it was a "disability" when it wasn't. As a general rule people who are alcoholics can't just "cut down a bit" (pretty much by definition) and have to stop drinking completely.
If this was just a one-time screw up with having a bit too much to drink and making a fool of yourself then you need to be honest about that with your employer - apologise and make it clear that it will never happen again. I'm not judging here, I'd imagine that most people who drink have had a moment like that. I know I have (albeit not in the work environment) and I only drink alcohol half a dozen times a year max!
On the other hand if you do feel that you have a genuine problem and this was just the incident that brought the problem to a head then I would say something like this:
I've realised that I have a problem with alcohol. I'm sorry for the impact this has had on the company and I'm seeking help to fix this and ensure that something like this doesn't happen again starting by doing x, y and z.
If possible make an appointment with a counselor or doctor (even if that appointment is after you'll be seeing your boss) and bring details of that appointment with you so you show you are taking steps to address the issue.
To be honest either way you're in a pretty crap situation and I hope you can work it out without too much damage to your work and life so good luck!