A lack of attacking ideas was the downfall for the Millers, and with them unable to test Goalkeeper Dave Button, making his debut for the Shrews - a goal for the Millers never really looked likely all night.
Speaking to Millersplayer, Moore said: "I don't think we have threatened their goal all night which was disappointing. It was an awful game but I feel we were a little unfortunate about the way the goals came about. We defended too deep for the first one and then the lad has smacked it in, and then they have had a lucky deflection at the end with virtually the last kick of the game."
Wade Fairhurst, on loan from Doncaster Rovers opened the scoring in the first half with Andy Warrington keeping the score down to 1-0 at half time with a penalty save from ex-Miller Dave Hibbert. James Devitt wrapped things up for Shrewsbury with a deflected goal two minutes from time.
Moore continued: "The lads have worked hard enough and I can't fault the work ethic but we didn't get the balls into the wide areas or test the 'keeper who was making his debut.
"When we did get our half chances we haven't hit the target. Kev has put one past the post and late on we had a decent chance, but it was the spark in the wide men that we missed, we didn't get them on the ball enough.
"We spoke before the game about getting in behind their defence. We have to finish our attacks when we get in behind their back four and tonight from both full back and centre half positions we played the ball straight down the middle. Alfie needs someone to get on the ball and play passes inside the full backs and we didn't do that. The use of the ball from the back was poor."