Looking to erase memories of their Boxing Day defeat, Pressley brought in Simeon Jackson and Frank Nouble to the starting line-up and both went close early on with efforts from inside the area which both forced visiting stopper Tommy Lee into action.
But the controversial moment of the first-half came five minutes before the break when Nouble picked the ball up on the left-hand side, cut inside and beat Sam Hird only for the defender to foul him what looked like inside the penalty area. The referee initially gave the Sky Blues a spot-kick but after consulting with his linesman, reversed his decision and gave City a free-kick outside the box.
City continued to monopolise the ball and Jackson went close again shortly after the break, after he cut inside from the left and hit a vicious effort which whizzed narrowly over.
Jackson was inches away again from the opener just minutes later when Nouble's cross from the left was headed by Gary Madine, and the striker's header from eight-yards was almost tapped in by the Canadian but for a Spireites defender to nick the ball off the line.
Chesterfield continued to defend stoutly but Aaron Martin went close as he smashed an effort from 25-yards which forced Lee into a good save to tip it wide of his right-post.
With three minutes to go City were agonisingly close to a winner when Gary Madine hit a low free-kick past the wall and against the post from 25-yards, with the Keeper rooted to his line.
But the visitors, who have conceded 31 goals in League One all season, held on to their advantage as the Sky Blues were unfortunate not to take all three points.
Coventry City: Allsop, Haynes, Webster, Martin, Pennington, Fleck, C. Thomas, O'Brien, Nouble, Madine, Jackson.
Subs: Burge, Willis, Pugh, Swanson, Finch, Tudgay, G.Thomas
Chesterfield: Lee, Darikwa, Hird (Banks 85), Gnanduillet (Jones 45), Roberts, Humphreys, Raglan, Clucas, Doyle, Boco (O'Shea 76), Evatt.
Subs: Wright, Gardner, Ariyibi, Talbot.
Referee: D Handley