The Blues had the first chance of the game in the sixth minute when Glenn Murray could only hit his effort from a Peter Murphy cross straight at Shrews keeper Glyn Thompson from only five yards out.
That proved to the best chance of the day for the Cumbrians as both defences took over the game and strangled the match out into the 0-0 scoreline it finished.
After 15 minutes good approach work by Steven Leslie and Marco Adaggio for the Salop outfit led to Ben Smith curling a shot over the United bar but chances were at a premium for both sides.
Steven Hogg volleyed a Duane Darby flick just over near the half-time mark as both sides struggled in the final third and went in level at the whistle.
Shrewsbury had a spell of pressure after the break with Darby and Hogg keeping Keiran Westwood busy in the United goal and ex-United centre-half Stuart Whitehead shooting wide from a corner as the home side looked for the opening goal.
Glenn Murray was replaced by youth-teamer Paul Gardiner on 55 minutes as the former Barrow striker, and scorer of United's second goal against Macclesfield on Saturday, felt a twinge in his groin.
Ten minutes later the Blues had a chance from a rare corner as Dan Kirkup looked to fire home from close range but Henry Goh was stationed on the line and was able to clear for the Shrews.
This was United's best spell of the game and Thompson had to be at his best for the home side to dive low and push away a Gardiner drive from the edge of the box.
The game then petered out in the closing stages and the result was confirmed late on as Westwood saved a lofted effort from Adaggio after Smith had played the ball over the top of the United defence.
All in all a useful point for the United second string although the lack of a killer instinct in the final third was again a problem which the first-teamers and youths are also struggling to overcome.
Shrewsbury line-up :
Glyn Thompson, Henry Goh, Stuart Whitehead, Gavin Cadawaller, Steven Leslie, Ben Smith, Jay Denny, Steven Hogg, Marco Adaggio, Duane Darby, Ciaran Lyng.
Subs : Jamie Haynes, Damien Stevens, Tom Sparey, Chris Morris, Adam Cain.
United line-up :
Keiren Westwood, Lee Andrews, Peter Murphy, Dan Kirkup, Simon Grand, Jamie McClen, Pete Ferris, David Beherall, Glenn Murray (Paul Gardiner 55), Raphael Nade, Shaun Vipond (Rob Bainbridge 85).
Subs : Matty Bell, Adam Bradley, Martin Graham.
Updated Reserve Team Table : Click here