Goalkeeper Tommy Lee had to make two early saves for Chesterfield at Coventry, from efforts by Simeon Jackson and Jim O’Brien.
The Spireites, fresh from their 3-2 Boxing Day win over Peterborough, pressed and Gary Roberts’ left-footer was just wide of the post.
John Fleck and Frank Noble both went close for Coventry, who had Jackson booked after 19 minutes for a bad tackle.
Gary Madine, on loan from Sheffield Wednesday, headed just wide for the hosts.
Roberts hit a 25-yard free-kick just over after Armand Gnanduillet was fouled, he was booked for his reaction to Martin’s foul, the City man also was shown a card for the challenge.
Dan Jones replaced Gnanduillet at the break and Doyle went as a lone striker. Madine and Jackson went close after the restart and Doyle tried to flick a Romy Boco ball in but hit air in a rare Spireites attack.
Jackson hit just over and Jones drove in an angled drive that deflected for a corner, Boco half volleyed just wide from the second phase. Charlie Raglan came to Spireites’ rescue twice, clearing a ball off the line from a scramble and then nicking it off Madine’s toes as he bore down on goal.
Boco hit high and wide after a Roberts burst through as the game entered the final phase. Madine hammered a 25 yard free-kick against the post on 88 as City ended the stronger but they were unable to breach the hardworking Chesterfield back line.
Chesterfield: Lee; Darikwa; Evatt; Raglan; Clucas; Boco; Hird; Humphreys; Roberts; Gnanduillet; Doyle.
Substitutes: Jones; Gardner; O’Shea; Banks; Talbot; Ariyibi; Wright.