Dean Holden put the ball into his own net in the seventh minute before a further strike from James Spencer and a Laurence Wilson penalty put the Shrimps three goals to the good.
Spencer was dismissed for violent conduct and the Shrews pulled one back thanks to Shane Cansdell-Sherriff, however it mattered little as Morecambe held on for victory.
Turner said: "We set ourselves a difficult task with the early goal. It was as bad a goal as I've seen with any team I've been involved with for a long, long time. There was a comedy of errors and it set everyone on edge.
"For the second we defended a set play badly and we could never get going. We've made two signings this week but we need players to improve our first team not our fairly large squad. Supporters aren't daft. They recognise where there are shortcomings and those we must put right.
"We had a go in the last 20 minutes but unconvincingly. We have to be honest, we are an easy side to play against. Teams are getting hold of the ball, passing it with some degree of precision because we're not doing our job right. This wasn't as bad as the defeat by Crewe on Monday because we did have chances, but against Crewe we didn't work hard."