In a bruising encounter, it was no surprise that the biggest men on the park were forcing most of the play.
Giant defender Mo Konjic came closest for Coventry from a Gary McAllister corner, but Ian Walker made an excellent save.
Then Gerry Taggart had two good efforts from Muzzy Izzet set-pieces after 14 minutes.
Izzet was pulling the strings for Leicester and had almost scored two minutes earlier with a free-kick from 25 yards.
And he came agonisingly close just before the half-hour mark when he ran onto Paul Dickov's flick-on and headed on to the bar with Morten Hyldgaard stranded.
Andrew Whing almost opened his account for Coventry when he was played in by Craig Pead, but his 20-yard drive whistled wide of Walker's right-hand upright.
After a scrappy first half, it was a goal of sublime beauty that broke the deadlock after just four minutes of second half action.
Konjic stole the ball off Dickov's toes in the six-yard box, but his poor clearance fell to Billy McKinlay 30 yards out.
The Scot had time, space and plenty of options, but chose to pick out the top-left-hand corner of Hyldgaard's goal.
The goal was a bright spot in an otherwise dull second period, with no other incidents of note until Leicester doubled their tally on 68 minutes.
A long ball from Walker found Callum Davidson in space and his cross found Jamie Scowcroft in space at the far post, where he unleashed an unstoppable drive from eight yards.
In response, Coventry brought on Matt Jansen and the on-loan Blackburn player took under two minutes to halve the deficit.
McAllister received a short corner and lifted the ball to the back post, where Jansen nodded across Walker for his first goal for Coventry, but the home side could not muster another goal to complete the comeback.