I think Kf4 is possible too. edit: actually Kf4 would be pointless I guess.
You're not the only one who sometimes misses such things in blitz :-) but in a slow game you would never overlook the fact that with Kf6 the king has wandered too far away to stop black from winning via ...f5 where white can't prevent black advancing a space every move and promoting.
Again yes i was playing blitz and lost... I didn't see this move which made me lose =(.