You did right, but not quite..
The AA all-in shove is a great move, when you are in a MTT vs an under_chipped playesr, or at a cash table where your stack and position, dominate; all other players automatically drop out, you see that a lot.
In your scenario, I did the same, pocket AA, shove, except three players shoved back. One guy turned his pair into a straight. lucky, but a winner.
One alternative to shoving with AA is to check-back, then the others players will show some of their strength by how much they bet.