Coleman was banished from the touchline for the second-half after storming on to the field to confront referee Steve Bratt, over the award of a Swindon penalty in first-half stoppage time.
Referee Bratt pointed to the spot four minutes into added-on time, after adjudging Leam Richardson to have handled on the edge of his own six-yard box.
Coleman's misery was compounded when defender Jack Smith stepped up to smash the resulting spot-kick into the bottom-left corner.
Coleman was forced to watch the second-half from the directors' box as Swindon sealed a crucial win, thanks to Andy Nicholas' third goal of the season three minutes after the re-start.
The tricky Ricky Shakes was hacked down on the edge of the penalty area and Nicholas headed home at the back post, from Aaron Brown's free-kick.
Accrington came into the match with the threat of a four-point deduction hanging over them after playing on-loan Preston midfielder Chris McGrail illegally in two games earlier in the season.
Coleman's hopes of a morale-boosting win never looked on and Swindon, chasing automatic promotion, could have been in front as early as the eighth minute.
Accrington goalkeeper Kazimierczak made a hash of a clearance and the ball bounced off Swindon striker Lee Peacock and cannoned back off the visitors' crossbar.
Midfielder Michael Timlin came close to breaking the deadlock nine minutes before half-time when he shot narrowly wide from 20-yards out.
Defender Ashley Westwood should have done better three minutes later when he headed wide from a Brown corner.
The home side had chances to add to their lead in the second period, with Peacock unlucky not to score when his close-range shot was saved by the legs of Kazimierczak.
It took until the 82nd minute for Accrington to seriously test the Swindon goalkeeper Phil Smith, when midfielder Jay Harris saw his 20-yard effort saved.
Accrington had defender Mauro Almeida taken to hospital at half-time with a nasty eye injury after being caught by Peacock, while Kazimierczak ended the game with concussion.