The Hammers suffered their second defeat of the season at Coventry on Monday night - and Steve Lomas was sent off in the final minute of the game.
West Ham started brightly enough and Scott Shearer cleared a backpass poorly straight into Teddy Sheringham's path; he tried to chip the ball over Shearer in the Coventry goal but it landed in his arms.
West Ham had another good chance when Sergei Rebrov raced forward on the break and stroked the ball to Sheringham on the right; he cut it back to Nigel Reo-Coker but the ball got stuck under his feet and the ball went into Shearer's arms.
Adam Nowland conceded a free kick just outside the penalty area, and when Michael Doyle floated it onto the head of Spurs-bound Callum Davenport for the highly rated defender to head home, the stadium erupted.
But, despite the announcer and the score board declaring Coventry had taken the lead, the goal was disallowed for an infringement.
Reo-Coker was booked for dissent and Louis Carey was booked for a foul on Matthew Etherington.
West Ham made the breakthough when Reo-Coker battled his way through several challenges and suddenly found himself with only the keeper to beat.
But he unselfishly squared it for Teddy Sheringham to stroke it into the back of the net at close range.
The lead was short lived, however; Brevett fouled Morrell just outside the box - for which he received a yellow card - and Doyle thundered the free kick into the top corner leaving Bywater clutching thin air.
Just moments into the second half Sheringham, who had fallen to the turf after an off the ball incident, went to remonstrate with Doyle as play went on around them, prompting the referee to stop play and give them both a caution.
Reo-Coker latched onto a loose ball and passed to Harewood who raced forward and struck a searing angled shot which Shearer parried with his feet.
Steve Lomas received a warm welcome from the fans as he replaced Adam Nowland.
Coventry made a double substitution with Barrett coming on for Wood and Suffo replacing Johnson; Luke Chadwick replaced Rebrov with Harewood moving up front.
Coventry took the lead after West Ham were unable to clear and Hughes's precision cross found Morrell, who volleyed home inside Bywater's right hand post.
With the minutes ticking away, Alan Pardew brought on Richard Garcia for Brevett, while Coventry replaced Morrell with Gudjonsson.
Garcia, back from a cruciate ligament injury, had replaced the suspended Chris Cohen as substitute.
Steve Lomas was sent off seconds from the end for an obscene gesture at the linesman which the latter pointed out to the referee. He was unhappy that, after gaining a few yards with the throw in, the referee then awarded it to Coventry City.
Sergei Rebrov was preferred to Luke Chadwick and played up front with Marlon Harewood moving to the right hand side.
Elliot Ward replaced Trent McClenahan on the bench.