"We have gone and shot ourselves in the foot and played into their hands. In trying to get ourselves back in the game, we went back to doing things we're not good at.
"We were getting the ball forward too quickly in our desperation to get a goal back. We're making life very difficult for ourselves and giving ourselves a mountain to climb.
"There's a bit of doom and gloom around and the lads just found it difficult to stick to what they are good at. That's the very disappointing thing about it - that they resorted to doing things they're not good at."
Aside from one move that saw sub Marc Williams and midfielder Robbie Garrett denied by Shrews' keeper Glynn Garner, the Dragons failed to stretch their opponents after the goal.
Carey said the Shrews' smash-and-grab victory was reminiscent of the Dragons' one-goal triumph at Gay Meadow last season.
"Apart from chances for Marc and Robbie Garrett, that was it really in the second half. I think Shrewsbury probably did to us today what we did to them at the end of last season."
But Carey was happier with his team's showing in a closely-contested first half, where both sides had opportunities to go ahead.
"I thought the first half was very tight - a typical derby game. There were a couple of chances at both ends.
"We probably shaded it in the first half in terms of chances. I thought if we continued and maintained that we could have gone on and got the goal."