Stanley went ahead through Terry Gornell early in the second half, but a James Collins double and a Mark Wright goal sealed the win for the Shrews.
Coleman said: "Shrewsbury didn't deserve to win that game 3-1. We created more chances but we`ve got to stop giving sloppy goals away."
"We were fortunate with the deflection for our goal and then we`ve gone to sleep, but they`ve been given a leg up. Shrewsbury had numerous free-kicks around the box which weren't free-kicks, and from one of them they got the corner which led to the first goal.
"We should defend better - but it wasn`t a free-kick we should have had to defend.
"There is no way Shrewsbury are in any way, shape or form a better team than us. I was the only manager complaining on the touchline. We can play better than that, but even though we can play better, we are still better than Shrewsbury."