KK with the big stack

[PrayingMantis]

5 left in a 27$ turbo. blinds are 100/200 ante 25, soon to become 200/400.

I'm first with 5300. Other stacks are 3200, 2200, 1500, 1400.

I'm UTG+1 with KK. UTG (3200) raises to 450. He's a pretty solid player. Other players don't seem to play so well.

I re-raise to 700. All fold. UTG reraises to 1400. I push. He calls with AA. I lose and am left with ~2100, and bust a few hands later.

After his reraise, I felt AA is a possible holding. Was calling and taking a flop, instead of pushing, a better play? Suppose we see a flop then, could I fold to an all-in bet, even if an ace doesn't hit? Am I too results-oriented?

My main concern is that I feel I was going for one of the first two places, with a big chance for first. And after this hand, I was in a very bad shape, that costed me a money finish, with the huge blinds coming.

Any thoughts? Or is it simply a KK vs. AA "bad beat"?