There's two ways to do it and it can't be done in multiplayer.
If you are given an automatic replay, you have to be quick. While it's replaying your shot there is a box in the lower left hand corner. I think it says VIEW REPLAY. Checkmark that box before the end of the replay and you'll be given the option to save it.
If you're not given an automatic replay but, want to save the shot anyway then after shot click on MENU. Then click REPLAY LAST SHOT.