Two goals from Shrews' teenage striker Tom Bradshaw cancelled out Tom Adeyemi's opener to secure their first victory in four games and get their play-off challenge back on track.
Turner said: "It would have been a travesty if we had lost the game. On the chances we created and the quality of our football we deserved to win it.
"We had a couple of very good chances in the first half, but we didn't take them and then a mistake by our goalkeeper led to Bradford's goal and Tom Adeyemi didn't half rifle it in for them, but our players showed a lot of character to bounce back from this setback.
"This isn't an easy place to come to. Bradford had not had the best of seasons, but the crowd lifted their players in the second half and they responded. You can see this as a difficult place to come to when they get it right, which I think they will do."
Source: PA
Source: PA