I hope someone who knows more about it can come on to help, but in the meantime, I would say that you should try to save him. I don't know what you mean by "just let him go," but most euthanasia techniques used for fish are pretty cruel, including flushing them (which I know you were planning to do when you thought he was actually dead. I just hope you don't do it while he's alive! Actually, flushing them is bad for the environment in any case, so I wouldn't flush him post-mortem either.)
I've been using Jungle Fungus Clear, which is quite cheap at Walmart, to treat fin rot on one of my rescue bettas. He had very advanced fin rot when I got him; I'm not sure how bad your guy's is. I also don't know if treating with a medication is good after the trauma of falling. So I hope someone with more experience is able to offer better advice, but in the meantime, I'd say hold tight. Often, treating a fish can be inexpensive and easier than you might think.
Good luck with him!