Blair Alston scored twice to hand the advantage to the Bairns and despite substitute Andy Ryan pulling a goal back for the hosts, they could not find a way back into the game.
Ryan could have made himself a hero but he somehow turned over Stevie May's delivery shortly after scoring the goal that put Accies back into contention.
"We ran ourselves into the ground and I couldn't ask any more from my players in terms of application," said Reid.
"We had an unbelievable chance to equalise, we are gutted for the young guy, it was probably harder to miss and that's the reason we are not in the semi-final of the cup.
"We are gutted and I think there's no doubt we at least deserved another chance at the game.
"I can look every one of my players in the eye - they gave me absolutely everything and are absolutely drained in the dressing room."