Posh had to survive a storm to claim all three points as Pools hit the woodwork three times in a game that could have gone either way.
Dean Keates curled home a free-kick to give Peterborough the lead before the home side hit back when Andy Monkhouse's low right-wing corner crept in. George Boyd slotted home the winner after Chris Whelpdale's shot was deflected into his path.
"That was some game. We hit the woodwork three times and had one or two cleared off the line - the stats alone show we deserved a draw from the game," Turner said.
"Peterborough are a very good side, especially strong in their attacking positions, and we have at least matched them without getting any reward. We played some good football, though at the beginning of each half it was Peterborough who were the better team.
"But towards half-time and towards the end we were on top, and while I'm pleased with the performance, I'm not at all happy with the result because the players have put in a great performance and got nothing for it."