Well you certainly ran into a hand there
Pre flop, spot on.
I never like to see a picture paired board on the flop when you hold an overpair. BUT its rainbow which means you can play it differently if you want to when you hold AA or KK (only those 2). Non rainbow and you must bet/go all in I think.
You can either check and hope the other guy bets (if he does he aint got it and youre good) then check raise all in. If he checks behind theres hardly a bad free card to give which is why you can trap here if you want.
OR you can bet a weak looking CB type bet like 400/500 and hope he makes a play at you and goes all in, then you call if he does. He may fold, obviously thats fine also. If he calls hmmmm, alarm bells.
OR you can just go all in and try and shut down the pot like you did. But by doing that you may only get called by a Jack here (or 33 obviously).
Thing is though with that good a pot I dont think you can ever really fold that hand with any conviction with these stacks, so its just a bit unlucky really. Youve no right to not think youre good at all.
The plays I mentioned above are to make more/save money in a deep stacked cash game really although you could use them in any game.