Charlton must win every remaining game and hope that Nottingham Forest, Barnsley and Norwich do not exceed 46 points to stay afloat.
The Addicks went into game with hopes of a win, after Coventry crumbled to a 4-0 defeat against Plymouth Argyle at the weekend.
But they failed to assert themselves and could only muster a single shot on target in a dreary game at the Ricoh Arena.
The first half was a particularly drab affair and both sides struggled to produce quality in the final thirds.
Coventry had the early half-chances with Michael Doyle heading an Isaac Osbourne cross over in the seventh minute. Minutes later, Kevin Thornton had a glorious opportunity to give the home side an early lead, but Charlton keeper Rob Elliot denied him.
Charlton, backed by just 387 fans, had their first opportunity through Zhi Zheng, but he could not properly test Keiren Westwood.
The visitors did have the ball in the net in the 22nd minute - but Tresor Kandol's header was ruled offside.
The second half saw an injection from pace from the Sky Blues. But despite several dangerous corners from Dan Fox, Elliot's goal remained untested.
Wales international Freddy Eastwood looked most likely to score for Coventry and, after hitting a 62nd-minute drive just wide, he nearly turned a Fox cross into the net with an outstretched boot.
Coventry introduced academy player Ashley Cain in the 69th minute for his debut - and he had two chances to make a dream start to his professional career.
First, he left the Charlton defence for dead - but saw his shot from eight yards blocked and then, with two minutes remaining, he raced through into a one-on-one only to put his shot inches wide.
Charlton's Nicky Bailey could have won it at the death - but his shot from inside the box rebounded off the post and away.