The match was largely devoid of both quality and chances with goalmouth action limited to a premium.
Miles Storey headed a cross from Ryan Woods over the bar in a rare Shrews raid during the first half while Vale also struggled going forward.
The hosts showed a little more ambition in the second period with Woods twice forcing saves from Vale's former Town keeper Chris Neal.
Connor Goldson headed a corner over the bar while former Wales international winger Paul Parry also dragged a shot wide of the near post.
Vale failed to force a single save from Shrewsbury keeper Joe Anyon, selected ahead of ever present Chris Weale by caretaker manager Mike Jackson, with their best effort a curling effort from Dan Jones which sailed wide of the target late on.