West Bromwich's five-game winning run was ended by a last-minute penalty by Viktor Gyokeres.
Alex Palmer was sent the wrong way from the penalty spot by Gyokeres, who scored his 11th goal of the year.
Jonathan Panzo had a good chance to win the game for the Sky Blues.
The home side is within a point of the play-offs.
After surrendering a three-goal lead againstSwansea on Saturday, Coventry had the better of the first half and showed no signs of being tired.
During a positive opening spell, Callum O'Hare, Ben Sheaf and Gyokeres all shot wide, while Gustavo Hamer and Palmer both made good saves.
At the other end, Tom Rogic and Jed Wallace were denied by last-ditch clearances and saves. Wilson was on hand to prevent Furlong from scoring.
The Seagulls looked to be on course for their fifth clean sheet in six Championship games before the Swedes scored from the penalty spot.
Mark Robins is the manager of the city.
We let in three goals and drew a game that felt like a loss after the players were outstanding.
We were unlucky not to score more against a side who have won five in a row.
It's up there with our best performance of the season. Expectations should not be going through the roof as people get excited.
We have a good group of players, but we don't have the depth of squad other clubs have. That's not something to complain about. It's down to the situation.
Carlos Corberan spoke to the radio.
In the first 70 minutes, they were superior to us. It was awful to lose the game because we had more control in the second half. The ball could not be cleared.
One of the basics of the game was lost to us. We have to recover in time for the game.
I don't know if it was a penalty or not but there were a few moments in the first half that made the referee want to whistle.
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