The home side hit back to earn a 2-2 draw which edges both teams a step closer to League One safety.
Lee Miller scored two spot-kicks for the Cumbrians, the first coming after a Matt Richards free-kick had given Shrews the lead, the second arrived just when it appeared that on-loan Charlton defender Yado Mambo's first league goal had won it for the visitors.
"It was a missed opportunity," Turner said. "I'm disappointed that we allowed Carlisle to get back at us after we scored.
"Judging from the reaction of the players the first penalty was a decision that shouldn't have been. The referee was unsighted for it and it was an amazing decision according to the players around."
Turner said of Carlisle's second penalty, awarded when Miller was sent tumbling by goalkeeper Chris Weale: "It sounds as if there was contact, but the lad was already on the way down.
"Our downfall was to allow Carlisle to get into those positions immediately after we had scored. Settling down on the journey home we will probably consider it a point gained, but right now it seems like two lost."