"It was a kick in the teeth," Carey told the official webiste.
"As I have just said to the lads, it not actually what happens here, it is the way that you respond to it.
"It looked like the game was going to be 0-0 and the point was cruelly taken away from us. We had a couple of chances, but I don't think that in the second half we didn't match the heights of the first half.
"Overall, I thought that we were well worth a draw. I thought that overall it was a solid, decent performance but we just needed that bit of luck to possibly have won it. I just thought that our quality in the final third was lacking a bit."
The winning goal came from Liam Dickinson in the 93rd minute and leaves Wrexham precariously perched 1 point above the drop zone to the Conference.