Despite taking an early lead through David O'Brien, the Ton crashed to a 2-1 defeat at New Douglas Park as a bizarre Gary Fisher effort and second-half screamer from Ziggy Gordon handed Billy Reid's side the three points.
Defeat leaves Morton two points ahead of nearest rivals Partick Thistle at the top of the Irn-Bru First Division but the Jags have now played two games fewer.
Keeper Derek Gaston was the culprit for the first Accies goal as he fumbled Fisher's corner and boss Moore was furious.
He said: "I'm disappointed with the display. We didn't start playing until we went down to 10 men after Willie Dyer was stretchered off with a dislocated shoulder.
"We got off to a great start but then we just sat back and played too many long balls.
"The condition of the pitch wasn't great but I thought Hamilton had more desire than us, which disappointed me more than anything.
"They are struggling to get away from relegation and we are trying to win a championship. He [Gaston] should have saved it. He is 6ft 2in. I don't care if he was fouled, he should have knocked people out the way.
"We have told him that all season. At the end of the day the referee didn't give a foul so it is not a foul. He should be dealing with it."
While Moore was left raging at his side's efforts, there was plenty of reasons to be cheerful for Reid as his Accies put further distance between themselves and the First Division relegation zone with a deserved victory clinched in spectacular fashion.
Reid said: "Ziggy has been here since he was 11 or 12, maybe even before that and I can't remember him scoring a goal.
"He is a right full-back who we played on the left hand side to play against David Graham, who has been really influential in the last few games, and I thought he won the battle convincingly.
"He has popped up and banged one in the top corner from 25 yards so all credit to him."