Here's how I play this in tournaments, I'm not saying it's right but its how I do it with a measure of success,
With an allin the most likely result is to pick up the pot preflop.
If the allin is called it either means you are beat AA KK or a slight favourite to AK or at best an underpair JJ 1010. There are two others in the pot so two possible callers making it twice(ish) as likely that someone has AA KK or AK.
I think an allin limits your likely outcomes to either taking the pot as it stands, being called with AA or KK, or facing coinflip with AK. A call from JJ 1010 or even AQ would be nice but unlikely.
For these reasons I call in this situation with QQ.
Then go allin if there are no overcards as AK should now fold and if he calls I'm favourite.
AA and KK have me beat, but if they bet first post flop it might give a clue.
If there's an A on the flop then I'll fold to a bet, or raise a bit if it's checked to me, if it's a K I'd think harder about my options.
The situation in the tournament isn't dire enough to rule out a post-flop fold so I may as well see the cards.
Of course none of that would have saved you here
Rex