Vale were much the better side in the first-half and were full value for a 2-0 interval lead with Chris Robertson's 23rd-minute header and a 30th-minute cracker from Jennison Myrie-Williams putting them in the driving seat.
Vale substitute Jordan Hugill's late goal finally killed off a spirited comeback by Shrewsbury, who had threatened an equaliser on several occasions after Liam McAlinden had reduced the arrears in the 59th minute.
Turner said his side were now under pressure to win their next two matches.
"We were poor in the first-half when most of our players stayed in their areas and didn't sprint around enough," he said.
"Port Vale are a strong side and good at what they do.
"We allowed them to dictate to us and didn't show enough desire. I looked at my watch and it was 38 minutes before we put three or four passes together.
"Our players looked frightened to make mistakes, but in the second-half that changed.
"We started to sprint about more with and without the ball and there were some encouraging signs.
"We got the ball in good areas at 2-1 down and it looked more hopeful, but we've ended up losing 3-1 and we are all disappointed.
"Our next two games are at home to Notts County and Oldham and they are now of paramount importance to us.
"It's imperative we take points from those games."