Salop were dominant for 57 minutes at Montgomery Waters Meadow in their first home game of the season, creating a number of really good opportunities to open the scoring.
But the complexion of the game changed when defender Tom Flanagan was sent off after receiving two bookings, just seconds apart.
The incident came about after Marko Marosi was involved in a confrontation with Tommy Leigh, pushing him to the ground. This caused chaos in the pental area.
Flanagan was awarded his first card for getting involved and his second card for retaliation.
And on 77 minutes Mitch Clark sent in a lovely cross and halftime substitute Tommy Leigh rose highest to head the ball into the corner of Salop's net.
Town boss Steve Cotterill described the decision made by the referee and the linesman as 'perplexing' and he believed the decision played a huge factor in the final result.
He said: "The sending-off has cost us the game.
"I still don't quite get it.
"I don't know how he can come up with two yellow cards in that little melee that's gone on.
"Tom Flanagan was booked for spinning the lad around, yes definitely a booking.
"But I don't see anything else, he's actually taking the lad away from Marko Marosi.
"I don't know how the referee can come up with two yellow cards in that space of time.
"You can't afford to go down to 10 men in the 57th minute, it's very, very difficult then to go and win the game."
After going down to ten men, George Nurse moved to the left side of the back three, and Jordan Shipley moved to left wingback.
And even though the game became more stretched, Shrews were coping well.
But their resistance was broken with more than 10 minutes remaining which would prove to be the decisive goal.
Town boss felt there was more his side could have done, to firstly prevent the cross, and secondly, to prevent Leigh from winning the header.
He said: "The cross could have been closed down by two players, not one.
"We've got on the wrong side for the header, we need to be inside him, not on the outside, that's why he gets a clear header.
"From our point of view, it was not very good at all."