I think the management have gone a bit over the top here. Yes, you were in the wrong, on a couple of issues, but being new to the role, any reasonable person would have given you the benefit of the doubt and just said �make sure you don�t do it again�.
Misuse of stock (IE stealing) is gross misconduct, and would get you sacked, without any prior warnings, but I don�t think you have gone so far as �misuse of stock� in the sense your employer means it. Your pouring it was a simple mistake; you shouldn�t then have offered it for �sale�, to anyone, but if what you say is true, there was no prior intention to �steal� the drink, nor defraud your employer, and this is the crucial point
You can�t start a formal unfair dismissal claim, but if you want to keep your job � and remember there will be some bad feelings, both ways now � write to your manager. State the case as you see it, admit you made mistakes, say you feel their response was a bit over the top for what was a genuine mistake, combined with not actually being told what you should do in these circumstances, and ask for a second chance. If that fails, and you wish to persist, if the pub is a managed one, write to the area manager, with copies of your original letter and any response. I would doubt they would reverse the decision, but if your manager has a history of dubious dismissals, your case may be added to the manager�s file and might help someone in any future, similar case.
To be honest though, I think you'll just have to put it down being in the wrong place at the wrong time, and move on. Annoying - yes, but don't let it get to you. Lots of people have downers like this happen in their careers.