McAllister got the passion he had demanded from his players, but they still lacked the killer instinct in front of goal.
The game was tainted by a horrific injury to former City player Colin Healy, who could have broken his leg under a late challenge from Youssef Safri.
Irishman Healy spent a loan spell at Highfield Road from Celtic two seasons back and left the field to a standing ovation.
Though Coventry had commanded the opening exchanges, Sunderland took an early lead after just eight minutes when Julio Arca burst forward on a 40-yard run as the Coventry midfield disappeared in front of him.
He played the ball wide to Stewart Downing who cut inside full-back Craig Pead and struck a low drive past the stretching Gavin Ward.
The goal came between two great efforts from Michael Doyle for the home side.
First he latched onto a ricocheted Patrick Suffo drive but blasted straight at Mart Poom, then when he met an excellent Stephen Warnock cross and forced a near-post save from the former Derby keeper.
Coventry hauled themselves back into the game on 21 minutes when McAllister played a sublime lofted throughball for Julian Joachim to chase.
With the ball heading out of play, Poom came off his line and brought the striker down and McAllister calmly converted the resultant spot-kick.
The second half failed to live up to the excitement of the first, the best effort coming from Sunderland substitute Marcus Stewart who blazed narrowly over from 20 yards.