After a festive week that saw them beat title rivals Partick Thistle and Dunfermline to move top of the standings, the Cappielow side suffered a 3-0 loss against the bottom-of-the-table Sons as the promotion race took another huge twist.
Moore said: "If you go one or two down against Dumbarton then you are in trouble as they are fighting for their lives.
"They were fighting at the bottom of the league more than we were fighting to stay at the top and that is what has annoyed me because that team has been magnificent for the last 13, 14 games.
"To produce a performance like that, especially after how hard we have worked to get to the top of the league, is bitterly disappointing. That is what makes football so interesting.
"We have played some really good football in recent weeks but we didn't play against Dumbarton."
It could all have been so different for the Ton if they had taken one of the glaring chances that fell their way inside the opening half-hour, but their profligacy ultimately proved costly as the league leaders left themselves with too much to do after the break.
It was Morton striker Peter Weatherson who could have sent the hosts en route to all three points but he twice passed up clear chances to hit the net.
On 20 minutes, Sons keeper Jamie Ewings parried a Scott Taggart drive straight into the path of the Ton No.9 but he couldn't convert, with the ex-Fir Park keeper producing a terrific save to deny the hosts the opener.
The shot-stopper was almost caught out just minutes later as he slipped after Weatherson was gifted the ball by Nicky Devlin, but Dumbarton were let off the hook once again, Weatherson this time curling his shot high and wide.
Moore's side were soon made to pay as the visitors netted twice in quick succession to bag a crucial three points and continue their renaissance under Ian Murray's guidance.
First, Mark Gilhaney fed Gary Fleming and he spun and finished well from 18 yards, his low shot nestling in the bottom corner of Derek Gaston's goal.
With the Ton still in shock, Dumbarton doubled their advantage. Jim Lister's cross was only partially cleared and Gaston couldn't deal with Scott Agnew's low drive as the ball trundled over the line.
In a bid to haul his side back into the game, Moore threw on Peter MacDonald and Tony Wallace at the break but it was to no avail as chances were again spurned.
Kevin Rutkiewicz missed from just yards out after Ewings spilled a MacDonald free-kick while Fouad Bachirou crashed a long-range effort off the bar.
It was left to sub Bryan Prunty to inflict the final blow as he fired in from 18 yards to give the Sons another crucial three points.
Murray, whose side are only three points off ninth-placed Airdrie, said: "The fixtures haven't been too kind to us over the festive period but to come away with six points is great.
"I said before these two games that I would rather be in Cowdenbeath and Airdrie's position but with our momentum and two games in hand I would rather be where we are."