Bradford's interim manager Peter Jackson reaffirmed his desire to take the job on a permanent basis after City slipped to a second defeat with him in charge.
Two goals from Shrews teenage striker Tom Bradshaw cancelled out Tom Adeyemi's opener in a 2-1 home defeat for the Bantams, while Jackson, appointed after Peter Taylor left the club a month ago, is expecting the club's directors to review his position again next week.
Jackson said: "You can't go on one game, but I know the situation and I desperately want the job. We didn't get the result we wanted. I cannot add to that. We need one or two wins to keep us safe from relegation - it might be more than that - and we've got some tough games coming up, but we'll regroup next week and look forward."
Jackson admitted play-off chasing Shrewsbury had dominated for much of the game, but he had been encouraged by his injury-hit side's display.
He added: "I thought Shrewsbury were the better side in the first half and our keeper Jon McLaughlin kept us in the game, but we managed to keep a clean sheet and when Tom Adeyemi put us in front I thought we were going to win it and we looked comfortable.
"Then we went to sleep at a throw-in to let them in for an equaliser and then conceded another goal. I was disappointed we dropped the points and came away with nothing, but I couldn't fault my players."
Shrewsbury manager Graham Turner insisted his side were well worth all three points and showed commendable character to turn the game round.
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."
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