Chances were at a premium in a drab first half, where there was little in the way of excitement.
George Porter's fierce drive flashed past the far post from 20 yards for Colchester, while Jabo Ibehre's shot on the turn flew straight at Shrews goalkeeper Chris Weale after Andrew Bond's pass into the area.
Shrewsbury had their moments as an attacking force and Steve McGinn's low shot flashed just wide, while David McAllister also went close.
The visitors started the second brightly and Jon Taylor poked the ball past U's right-back Brian Wilson before drilling in a shot which goalkeeper Sam Walker saved at his near post.
Walker turned McAllister's fierce 30-yard thunderbolt away for a corner just after the hour, as Shrewsbury threatened to take the lead.
Both sides probed away in a bid to find a winner and Shrewsbury looked the more likely to score, but in the end the spoils were shared.