He was already pissed and crazy. That why he was abandoned in the first place. It’s also why he was floating on that derelict cryoship. Kirk was justified. Earth of the past was justified.
Well, he had reason to become more pissed and crazy.
Earth of the past chickened out of solving its problem. What was done wasn't observing humane (in case they decided he deserved a humane treatment), and wasn't effective either (in case they didn't).
Did he? Or did he do the humane thing as befitting a Starfleet officer? Just because it didn't turn out well in the end doesn't mean he was in the wrong to do it. He was in the wrong never coming back to check on Khan, especially when he left one of his crew behind.