Summer signing Denis Behan bagged his first goal for the club since signing from Cork City but Pools suffered their second home defeat in four days courtesy of goals from Aaron Lescott and Jo Kuffour.
Turner said: "We are all disappointed. We didn't deserve to lose that game but I suppose that's football.
"I thought we looked like scoring a lot of goals but the luck didn't run for us at times.
"I was delighted with Denis Behan, who has been our best player so far this season, and it was great to see James Brown back after nearly a year out."