Michael Mackay eventually did find the back of the net, but Pools were already 2-0 down after second-half goals from Leon McSweeney and James Vincent.
Turner said: "I thought we created a lot of chances throughout the game so it was disappointing that we didn't score until it was too late.
"The pitch didn't help us play, but we all know about that here. There were a few things to be positive about, but overall I suppose it is another disappointing night for us.
"We've got another tricky trip to Cheltenham to come on Saturday."