Bad beat or bad play?

[ZManODS]

First time playing a real table game at Turning Stone.
3-6, mix of players.

Im dealt A7o on the button.
Few callers, like 4 and i limp in.

Flop comes. K77 rainbow
Someone early bets and everyone calls but 1, including me. (Im trying to save my raise for 4th street)

Fourth Street. 6 (K77)
Everyone checks but the person before me, he bets. I raise. EP player folds so its me and the persone ahead of me. He re-raises so i call.

River. Blank
He bets i call.

He shows me his 66 for a full house of 6's over 7's
I muck my three-of-a-kind Ace high.

Did i play correctly, incorrectly? Any comments?

[butters]

fold preflop. A7o is only going to get you in trouble after 4 limpers.

[Homer]

Preflop: I would have folded.

Flop: Fine.

Turn: I would have capped.

River: Given that you called the turn three-bet, I would have raised the river. However, I think capping the turn and taking it from there is the better play.

-- Homer

[Ed Miller]

Other than failing to fold your cheese preflop, I think you played fine. I personally would have raised the flop to a) get more money in the pot, and b) hope that people don't give me credit for a 7.