Charlie Taylor's last-minute leveller grabbed a point for the struggling Bees to keep them out of the relegation zone after a Mark Hughes own goal looked like handing the promotion-chasing Shrews victory.
Turner, whose side are without a win in five matches, thought Shrewsbury deserved more.
"We were worth the three points and the game should have been over before their equaliser - it's two points that have escaped us," he said. "We can pass the ball better than we have done here and it's disappointing to lose the win so late on in the game."
Turner added: "I want to bring in two more players before the transfer window closes because we've got a few injuries at the moment and we need to bring a few in.
"But with Accrington coming up on Tuesday it doesn't really give me a chance to get any in before that so we're down to the bare bones."