Sounds terrible, but accidentally chopping off the last few cms of a snakes tail isn't the worst thing you can do. I've known of several snakes who've happily lived after loosing most of/all of their tail.
Obviously keep an eye out for any breaks in the skin or kinking, but at its worst, a damaged tail is hardly a life threatening occurrence in most cases.
I've heard of a snake who had lost their tail right up to the vent (large BHP). Not sure on specifics other than this snake was seized from a bad situation with the tail already healed over. Snake was male, and worst outcome for him was that he was essentially castrated :/
Might be more of an issue on an arboreal snake who depends more on their tails, but most (particularly younger animals) will take to change much more easily.
That all being said- your snake is most likely fine! Probably just a sore tail