The Irn-Bru First Division leaders travelled to Dens Park in high spirits for their William Hill Scottish Cup fifth-round clash with the SPL basement boys, fresh from last weekend's 1-0 triumph over Raith Rovers.
However, after going in for half-time tied at 1-1 – thanks to a goal from Michael Tidser just 90 seconds after Jim McAlister's opener – the Cappielow side capitulated, losing four goals in a dreadful 17-minute spell.
And with four of the home side's strikes coming from either corners or free-kicks, the focus of Moore's anger was clear to see.
He said: "I'm disappointed with the goals we lost because we have been defending set plays and corners really well this season, and that was our undoing.
"Four goals from dead balls is not good enough – if you have someone to pick up at a set-piece, it's your job to make sure they're not on the end of the ball. We didn't win the first header, and we didn't pick up the loose ball."
Many supporters predicted a cup upset yesterday afternoon with table-topping Ton in line to swap places with Barry Smith's men this summer.
Their task wasn't helped on 29 minutes though, as McAlister latched on to a Nish knock down to rifle under Derek Gaston.
And despite the false hope that came from Tidser's close-range effort soon after, Morton's second-half showing failed to impress as they struggled to cope with the aggressive play of the hosts.
On-loan Celtic starlet Lewis Toshney started the Dens revival with Nish, John Baird and Declan Gallagher all adding insult to injury for Ton.
"We managed to get a goal back straight after they scored and that gave us a lift. We were hopeful at half-time we could try and do something," admitted Moore, who will now try and lift his troops for league game with Airdrie this weekend.
"We fancied ourselves to do something, but when you only have two players who turn up then you're not going to win any game.
"Michael Tidser got pass marks, and for spells in the game Peter MacDonald did up front. The rest of them just didn't play.
"In the first half I thought we played within ourselves, we didn't have any drive."