1/2 Live AA hand... I really donked this up.

I'm sitting with 450 on a 200 max 1/2 table at Winstar in Oklahoma... Only one person on the table has me covered, and he is the hyper aggresive type... I look down and find AA and raise it to 20 in MP. There were about 2-3 limpers before me and a total of 3 others called the 20 to see the flop. The flop came QK4 and small blind bets 10, I raise to 35, and he makes it 60... Here I'm thinking he has KQ or possible just AK/KJ as I said he was very aggresive.

Turn comes a 4 and he grabs 100 and bets it into a pot of only about 140... At this point I'm very confused, but I think for a minute and realize that he does not have QQ or KK for sure, and still I put him on KQ and I know that the 4 counterfeits any two pair he has except one with a 4. I then move in for my remaing 200+. He calls instantly and turns over Q4 and I'm done...

Did I play this hand TERRIBLY, and if so how could I possibly have gotten off of it that easily.