Just a bad beat?

[Diesel10]

Normally I chalk these things up to sh*t happens, but I can't get this one play from last night out of my mind. Did I play this wrong or is it just a bad beat?
$50 SNG, middle of game, 5 players left, all playing fairly tight
Chip Leader =6500
Me= 3500
3 others all less than 2000 each
Blinds 75/150
UTG I get AA
Raise to 500
Chip leader, one to my left, calls.
Everyone else folds.
Flop is AKQ rainbow-
I bet 200 with my set of Aces hoping for a raise and get one as he pushes all-in. I actually think about this first and conclude he must have middle or bottom set or maybe two pair. I call. He turns over JT. Turn and river are blanks and I'm out.
Should I have pushed harder pre-flop? I didn't think I was slow playing, I wanted to push out drawing hands but maybe keep some in who I could dominate. I can't lay down a set of Aces can I?
Like I said, I keep thinking that this is just a bad beat, but there is also this tiny whisper in my head that thinks maybe I should have played it differently- can't let it go.
Thoughts?