The Latics raced into a 2-0 lead inside the opening 26 minutes at the Greenhous Meadow and were soon three goals to the good as strikers Danny Philliskirk, who scored twice on his debut, and Adam Rooney proved too hot for Shrews to handle.
But Oldham continued to look dangerous going forward and lively Dutch winger Sidney Schmeltz hammered home a deserved fourth to seal the visitors' superiority 15 minutes from time.
Turner said: "You cannot play football standing still and you cannot play football at half pace, especially against a side as lively as Oldham.
"The game was over in the first half-hour and the disappointment was that there wasn't a sprint in us in that period, which is unusual.
"But we have to learn from that because in that first 30 minutes I thought it was the most inept performance we've put on for a long, long time here."
Turner, though, had sympathy for back-up goalkeeper Joe Anyon, who was beaten four times on his first senior start for nearly a year after being selected ahead of first-choice stopper Chris Weale.
"The people in front of him let him down," Turner insisted. "I don't think we could cope with the movement and ability of the Oldham front four. It's one thing we've got to get used to."