It might root on it's own, and it so, it might take a long time, so don't give up on it yet. Keep it dry.
In the future, let the pup grow out on the cactus more before removing it, as they do root pretty consistently if they're just a bit bigger than you have. If you have a source to take a cutting from the mother plant (without damaging someone else's property- ask if it's not yours), you should be able to root that for sure. I've had luck with most cuttings over a couple inches long.
Best of luck with it.