In blustery conditions, the Sky Blues started the League One clash at a ferocious pace and could have taken the lead when Chuba Akpom's strike inside the penalty area flew narrowly wide.
But the first clear opening fell to the visitors in the 20th minute when a mistake from Dan Seaborne presented Tom Eaves with an easy chance but goalkeeper Joe Murphy denied the striker from eight yards out.
The second half had few opportunities, but Eaves was guilty of missing another glorious chance in the 62nd minute, this time heading wide from five yards out following Ryan Woods' centre.
Michael Petrasso then missed a good chance for the Sky Blues with 14 minutes to go when he blazed his effort over the bar just inside the area following Callum Wilson's flick.
Shrews could have stolen three points but Murphy was on hand again to deny David McAllister inside the area. The draw leaves Shrews three points from safety and unbeaten in their last three games.