Shane Lowry's header gave Millwall a win which leaves Coventry on the brink of relegation from the Championship.
Coventry's Gary McSheffrey saw his penalty saved by Maik Taylor just before the hour.
Ten minutes later Lowry headed in to earn the Lions the win.
Coventry are five points adrift of 21st-placed Bristol City with only two games remaining and look set to drop into the third tier for the first time since 1964.
The Sky Blues now face already-relegated Doncaster on Saturday before heading to Southampton on the final day and they must win both games to have a chance of survival.
Clive Platt wasted a good early chance when he planted a header over from Sammy Clingan's cross.
Clingan's free-kick was saved by Taylor and Oliver Norwood also thumped over as the hosts searched for a breakthrough.
They looked set to be rewarded for their pressure when Cody McDonald won possession on the left and burst into the area before being brought down by Taylor.
But the 40-year-old goalkeeper pulled off a fine save to push away McSheffrey's spot-kick.
They were made to pay when Lowry headed in from Alan Dunne's cross as he earned the Lions a fourth straight win with his first goal for the club.
Coventry manager Andy Thorn: "At the moment I feel angry and all sorts. I'm disappointed when I look at people and I see how much effort they give, what's been done and where we've been left. The whole lot."
"Every time we've put the players on the pitch they've been bang at it, they've given their all for me and for the club - we just haven't had enough of them.
"I'm angry because I see the hurt in the players when they give everything but they've had no help, we've had no help, full stop. So that's where we are, that hurts.
"The lack of resources, the close season and early part of the season up until Christmas has killed us."
Millwall manager Kenny Jackett: "I thought we didn't play as well as we have been playing and Coventry missed a number of chances.
"My goalkeeper [Taylor] I put down as man of the match, which tells its own story of the game.
"It wasn't a fantastic performance by ourselves after the emotions of Saturday, getting to 50 points and mathematically being safe from relegation."