The Shrews have not won on their travels all season and a record of just three points from 10 away games has left them in trouble near the foot of the League One table.
Oldham earned victory with a 13th-minute goal from Jonathan Grounds, who slotted home from six yards after goalkeeper Chris Weale palmed out Matt Derbyshire's low cross.
"Our away record is a concern, absolutely, and we were talking about it in our hotel on the way up here," said Turner. "We've taken 15 points from our home matches this season, so three away points out of 30 is unacceptable.
"You could see from our second-half performance that it isn't down to a lack of effort, so maybe it's a lack of confidence. All we can do is keep playing and keep believing that it's going to turn around for us.
"This game was a lost opportunity because we should have come away with at least a point. Our second-half performance was decent. We had a lot of the ball and got into good areas, but we didn't have the finish. The goal we conceded was disappointing because we knew Oldham would start the game quickly and we should have dealt better with the cross."