Graham Turner's men were never at their best although they fashioned several half chances in a frantic second half.
Tom Bradshaw and James Collins both fired over from outside the penalty area while a Matt Harrold cross-shot was fumbled by Accrington keeper Alex Cisak.
But Stanley defended well with central defenders Phil Edwards and Sean Hessey excellent as they collected a 13th away draw of the season.
Accrington had the better of a low key first half and so nearly made the breakthrough in the 19th minute when home goalkeeper Ben Smith made a tremendous double save to deny Luke Joyce and Sean McConville.
Shrewsbury, in contrast, were riddled with nerves and, apart from a Collins effort into the side netting, there was nothing to concern Accrington keeper Cisak.
Source: PA
Source: PA