Steven Pressley's side did at least manage to stop the rot by ending a run of three straight League One defeats, but they were unable to break down a determined Shrewsbury side who showed great resolve in Michael Jackson's second game as permanent manager.
Coventry striker Chuba Akpom had the best chance of the first half inside the first three minutes, the 18-year-old firing a close-range effort narrowly wide following good work from Callum Wilson.
Akpom was involved in most of the hosts' best openings and he went close again 10 minutes before the break as he shot over from a tight angle.
Yet for all Coventry's pressure, it was the visitors who should have taken the lead midway through the second half when striker Tom Eaves failed to hit the target with a header from point-blank range.
That proved to be the last true clear-cut opportunity of the contest, which meandered towards its conclusion and another disappointing result for Coventry.
The draw leaves Shrewsbury three points adrift of safety in 22nd, while Coventry are only three clear of danger in 13th.
