Shrewsbury earned a point on the road after playing out a 0-0 draw at Exeter.
Town had the chances to win in Devon with Max Mata seeing a close-range header saved by Vil Sinisalo.
The goalkeeper then went on to make an outstanding save in the second-half to keep out a fierce Dan Udoh strike.
Town entered the game at St James Park with 10 players in the treatment room with Tom Flanagan, Morgan Feeney and Taylor Perry all picking up knocks during the win over Port Vale.
There was some good news, though, regarding Flanagan - with his knee injury not as serious as first feared.
It means the centre-back is now expected to be out for months rather than the rest of the season.
With so few players available, boss Matt Taylor opted for a 3-4-3 formation that saw Dan Udoh, Max Mata and Ryan Bowman all start in attack.
Aaron Pierre also made his first league start since returning to the club with the 30-year-old joining Chey Dunkley and Joe Anderson in the back three.
Elliott Bennett and Jordan Shipley were the wing-backs with Carl Winchester and Nohan Kenneh in central midfield.
Youngsters Nana Owusu, Isaac Godwin, Jack Loughran and Luca Whitney were all named on the bench.
Exeter lined up in a 5-2-2-1 system that saw Dion Rankine and Jack Aitchison start behind Cheick Diabate in attack.
It was Town who flew out of the blocks in Devon with Taylor's side creating a number of chances to open the scoring inside the opening few minutes.
First, following a corner, the ball fell to Shipley who fired narrowly wide from 18 yards.
Bennett then whipped in a dangerous cross aiming for former Grecian Ryan Bowman, but City managed to scramble it away.
Moments later, a long throw was flicked on by Chey Dunkley towards Mata. But his header was claimed by goalkeeper Vil Sinisalo.
It was in the 12th minute when the hosts created their first chance when a deep cross found Diabete who headed over.
Another player was then added to Town’s ever-growing injury list when Bennett was unfortunately withdrawn in the 25th minute.
Exeter went on to have a spell of pressure that saw Yanic Wildshut's and Ryan Trevitt's decent efforts goalward from outside the box well dealt with by Marko Marosi.
It was Salop, though, who almost went into the break ahead when, just before half-time, goalkeeper Sinisalo claimed Anderson's effort following a goal-mouth scramble.
The first chance of the second half came the Grecians' way when Cole’s free-kick from just outside the box hit the post.
Town, though, then went on to create two excellent chances - both of which fell to Udoh.
First, a quick-paced counter attack saw Shipley win the ball back before laying it off to Winchester. He then drove at goal before slipping in Udoh who fired just wide.
Then 10 minutes later, Bowman lifted the ball over the top for Udoh who drove forward before unleashing a great strike which was matched with an even better stop by Sinislao.
In the same minute, the ball broke for Winchester in the box but his effort was well blocked by Will Aimson.
From that point both teams pushed for a winner to no avail - with Salop going on to take a good point back to Shropshire.
Exeter City: Vil Sinislao, Zak Jules, Will Aimson, Ryan Trevitt, Reece Cole (Tom Carroll 77’), Yanic Wildschut (Vincent Harper 86’), Ilmari Niskanen (Harry Kite 86’), Dion Rankine (Kyle Taylor 67’), Pierce Sweeney, Jack Aitchson, Cheick Diabate (James Scott 67’)
Unused Substitutes: Shaun MacDonald, Alex Hartridge
Shrewsbury Town: Marko Marosi; Joe Anderson, Aaron Pierre, Chey Dunkley; Jordan Shipley, Elliott Bennett (Tunmise Sobowale 24’), Nohan Kenneh, Carl Winchester; Dan Udoh, Max Mata (Mal Benning 89’), Ryan Bowman
Substitutes: Harry Burgoyne, Nana Owusu, Isaac Godwin, Jack Loughran, Luca Whitney
Referee: Alan Young
Attendance: 5,288 (169 away)