NEARLY costly error in 5/10...

I am in SB with KQ and 2 callers, then I just flat call and the BB checks. Flop comes A 10 K, and I check. BB bets, and I certainly cannot put him on any ace, as he has been raising them all night... Everyone else folds. Then I bet into him on the turn and of course get raised...

Moral of the story is that the river comes a K and I bet out knowing that he'll check behind me... He calls and says "You hit your king didn't you?" I'm sitting in seat 1 and he's in seat 2, so I just flipped my cards up so he could see them, then apparently I flipped them back down into the muck. The dealer then awarded the pot to him, but he was a very nice guy and gave it to me. I offered to give him $25 for being nice, but he refused.. I'll certainly buy this guy a hot dog or something next time I see him.