The Shrews boss saw his side lose 2-1 to a dramatic stoppage-time winner from James Hanson. The tall striker seized on a loose ball after the visitors failed to clear James Meredith's cross and lashed the ball into the net with a right foot shot to crown a stirring comeback after City had gone behind in the second minute.
Bradford suffered another blow when they lost leading scorer Nahki Wells after 23 minutes with an ankle injury after a heavy challenge from defender Dave Winfield.
But they responded well before half time when skipper Mark Jones and substitute Mark Yeats had goal-bound shots blocked in a frantic spell of pressure and goalkeeper Chris Weale made a superb save from Kyel Reid.
Reid equalised in the 60th minute from Yeates' cross and the match appeared to be heading for a draw before Hanson's last-gasp winner.
Turner said: "We have got to look at ourselves and see why we concede goals so late in the game.
"Bradford are a very direct side, knocking the ball up to the front player (Hanson) and playing off him, but we have got to deal with that.
"I don't think we played as well on the ball as we could have done in the second half, but then we played a little ball over the top to Tom Bradshaw and he should have done better with it.
"I cannot complain about the players, but we have got to be stronger mentally to deal with situations like this in front of big crowds like Bradford get. No one will give you anything in this league. We have let a lead slip too many times this season."
Turner said the decision to send off Winfield looked to be very harsh, adding: "The lad has sent in a great shot and our player has made a great block and to send him off was beyond my comprehension.
"After that it was back to the walls for us, but we should have capable of hanging on to a 1-1 draw."