Having pushed their luck for 93 minutes, they could hardly complain when Matt Gooden ran past leaden-footed defenders to glance in a header, but it stung all the more because of the way they had built hopes of smash-and-grab up.
Until then, it had looked as if no one was going to beat Lee Nicholls. When he was not making saves, Coventry were wasting chances, Jamie Allen hitting the post and Danny Hyam heading wide at a second-half corner.
But it looked like Huddersfield were going to get away with it courtesy of Danny Ward's tidy 19th-minute finish. They were not. They have now gone four games without a win.
Scott High and Lewis O'Brien worked the ball out to Harry Toffolo, who pulled the ball back to the edge of the area, where Ward drilled the ball in after 19 minutes. It was the sixth time in the past eight games the Terriers had opened the scoring.
Not long after Nicholls received treatment he was caught overplaying, passing a ball High did not want with Callum O'Hare at his back but the forward was unable to lift his chip over the goalkeeper. There were cheers when he kicked the ball long shortly after.
There would be another poor kick later but in between time he made a great reflex save, sticking out his right foot when Todd Kane got into the right corner and pulled the ball back for O'Hare. The good, not the bad and the ugly, would be more typical of his day. He deserved better than to be denied a clean sheet.
Coventry looked like they started in more of a back four but their formation quickly morphed into a copy of Huddersfield's 4-3-2-1 and they looked the livelier of two sides who have exceeded expectations this season, but just dipped lately, dominating possession and having more and better chances.
The Terriers looked like they had bucked their ideas up at the restart, Josh Koroma playing a wonderful ball and Simon Moore just touching Duane Holmes's shot wide, then Sorba Thomas - again looking like a man in need of a rest - flashed a cross in front of everyone.
It was only five minutes, though, and ended with Allen crashing an effort against the upright.
How much was Huddersfield sitting back, how much was them not being allowed to do anything else was hard to judge.
Koroma did produce a lovely outside-of-the-boot cross which ended in a corner, but most of the action was at Nicholls's end.
He made a great tip-over from Hyam's header at a Kane free-kick, then saw the defender miss the target from his next effort. In between time, substitute Tyler Walker failed to get a clean contact on his effort.
Matty Pearson, who had missed a good header when High's blocked shot ballooned to him, made up for it with a touch on Ian Maatsen's effort. Jodi Jones curled a shot into Nicholls's midriff.
Huddersfield Town: Nicholls; Pearson, Lees, Colwill; Thomas, High, O'Brien, Toffolo; Holmes (Ruffels 90), Koroma (Turton 61), Ward (Campbell 71).
Unused substitutes: Rhodes, Sarr, Schofield, Russell.
Coventry City: Moore; Hyam, McFadzean, Rose, Dabo (Maatsen 62); Kane, Kelly, Sheaf (Walker 62); Allen, O'Hare (Jones 81); Godden.
Unused substitutes: Wilson, Gyokeres, Shipley, Eccles.
Referee: J Smith (Lincolnshire).