High-flying Rovers' attempt to avoid a third straight league defeat suffered an early blow when Liam Palmer was sent off for a lunging tackle in only the sixth minute.
Chris Porter, on loan from Sheffield United, pounced on an error from goalkeeper Owain Fon Williams to put the relegation-threatened Shrews ahead before Cameron Gayle headed in his first league goal in the second half to seal back-to-back wins on the road.
"On paper I think we could have won - 11 versus 11 and we win the game, I don't think there's any doubt about that," Moore said.
"I still haven't seen it. Some people are saying it was a sending-off and some are saying it's not, but it no doubt affected the game.
"I sound like Arsene Wenger really as I haven't seen it but to me it didn't look like a straight red.
"So we're down to 10 after six minutes, but you can't legislate for what our keeper's done there, he's been fantastic all season."
Rovers face Swindon next, and Moore added: "We can't feel sorry for ourselves - we've got to get on with it. We've got a hell of a team to come here on Tuesday and we go down to 10 again we'll get beat.
"The tempo was there but the second goal from a set-play was so frustrating as we've been working on them."