I would not forgive, or at least I wouldn't forgive and remain in the relationship is probably more accurate. However, I have my own reasons for that based on my own world view and everyone is different. In some cases I think relationships can, and do, overcome infidelity and become stronger for it.
Overwhelmingly, however, the solution lies with the unfaithful partner really addressing the root cause of their behaviour. The answer is not being having their movements curtailed so that they don't face temptation. The point is that temptation is always all around is - it is the ability to resist temptation that matters.
There are lots of ways to 'affair-proof' your relationship. The most fundamental starting point is self-reflection. Your partner needs to look at his own inadequacies and insecurities - what it was about this drunken ONS that fed into those insecurities and urged his drunken mind to give himself permission?
The main thing is that he should be the one going through this process in a bid to regain your trust. If he's not doing that and simply doling out platitudes like "It didn't mean anything/it's you I love/I won't do it again/I'll do whatever you want@ - well I'm not surprised you don't have the trust back. The "I'll do what you want is a particular copout because it puts all the responsibility back on you to fix things.
I'm so sorry you're hurting right now. 