Deyvsonflp.
How did you review your play in this hand afterwards?
I think the first thing you should consider is your decision to limp with AA. While this is an often seen play, in any event you are allowing the BB to see the flop for nothing! What this means is that your best hand (pre flop only) is now up against ATC, and while favourite pre flop, could change dramatically once the flop lands.
As it is, the BB shoves and you have no alternative but to shove too. So now you are at the mercy of the board. You are not in any form of control and can not influence the hand at all. Probability takes over and as you discover, not being in control means you just have to watch the tourney float away from you.
Best wishes
BB