Jon Taylor but the Shrews ahead midway through the first half but on-loan Middlesbrough striker Charlie Wyke levelled before Pools had goalkeeper Scott Flinders to thank for some late heroics, while Tom Bradshaw also struck the bar for the hosts.
Shrews boss Turner said: "I felt we probably did enough in the last 15 minutes to have won it. We were unlucky as two outstanding saves from the goalkeeper and the underside of the bar stopped us getting all three points.
"But before that, for some unknown reason given the run we're on, I couldn't understand why we were so cautious.
"The number of times we gave the ball away was worrying. We lacked any sort of composure in that first hour or so but you could see how we can do it in that final 15 minutes when we really had a good go at it.
"We passed the ball with some precision, we got ourselves into good areas and we should have won it."
Turner stressed there were some positives to emerge, notably another goal for highly rated young winger Taylor - his sixth of the season.
"He's been a threat down the right and has ended up up front where he's been equally a threat," he added. "He's having a good spell at the moment and he's got to keep that going for us."