Luke Summerfield's header on the stroke of half-time earned relieved Town only a fourth win of the season, with the three points enough to lift Turner's men out of the League One relegation zone.
"We were desperate for that victory and it should do the confidence a bit of good," Turner said. "You could see the fragility of things late on in the game but we broke quite well and maybe should have done better.
"We defended well but you could see the anxiety, we were dropping deeper and deeper, but it's such a relief to win and get the three points to climb out of the bottom four.
"We know where we are, we know what we're about and it's about building on this victory if we can."
But Turner admitted his team may have received a lucky break with a big penalty call which went in Shrewsbury's favour before the goal, with Lauri Dalla Valle appearing to be barged over in a congested area. He added: "I was thankful he (the ref) didn't give anything."