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."
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."