His mistake wasn't putting his hands on him, it was not being more forceful. People like that (not blacks, thugs in general) only respect force. When the guy got up in his face he should have tried to neutralize the first guy before the other two jumped in. People like that feel safety in numbers. You can't really fight off three people normally, so your best odds is to try and completely fuck one of them and hope the message is sent and the others back off. If it doesn't work, and the other two jump you, try to focus on one of the two and fucking him up.
All this is good on theory of course, and much easier said than done. There is a very good chance you're going to get fucked up, but he got fucked up anyway so at least you give yourself the best chance by meeting force with more focused force.