Couple of things to think about:

1) It's okay to go broke with AK. You basically lost a coin flip, there are worse ways to bust out.

2) If you raise with AK and get two callers, it is profitable to only fire again if you hit. I'm not saying that's necessarily the best line, but it is +EV.

3) I believe it was CSC who pointed out that check-raising all-in with AK in a spot like this can yield some increased fold equity, as your opponents may put you on a big pair. My gut tells me that wouldn't have mattered here, though, as this guy was going to get it in with his 77. Checking and folding to a large bet or calling a small one hoping to hit one of 15 cards (club, A, or K) on the turn wouldn't be bad either.