Do you call here?

Late in a $135 buy in 40 player tournament. There are 7 of us left, blinds are 2000/4000. 4 people are getting paid, 1st is 2100, 4th is 500. I have about T15000, and I have an about average stack in terms of the people left. Needless to say with the blinds so high in terms of the average stack size it had become an all-in fest.

Chip leader goes all-in UTG. I'm in the button with 44 and everyone else had folded (a couple people out of turn). Based on the previous 4 hours of play with this player I am very confident that he has overcards and not a pocket pair. I call because I figure I am ahead (though slightly) and if my 4's hold up I'll be in good position to finish 1st or 2nd.

He has AK and a king comes on the flop and I lose.

I knew the best I could hope for was 50/50 when I went into it but I am trying to analyze whether I should have made the call. I am not used to playing in the bubble with the blinds so high.

I pushed with worse hands then that in order to stay alive but calling is a different story. Do you call here if you are sure villian has overcards? Why or why not?