Bruce was relieved of his duties last month after a 2-1 home defeat to Wigan, before Martin O'Neill was named as the club's new boss.
"It wasn't specifically the last home game against Wigan that determined we would change manager, because we outplayed Wigan for most of the game," Short said.
"However, once again, things didn't go our way and ultimately we were left to reflect on the fact that, over a long period of time, we have been underperforming.
"We believe the club should be in a better position and consequently the board took the action we believed was necessary for the good of the club."
Martin O'Neill celebrated his first game in charge of the Black Cats yesterday with a 2-1 victory over Blackburn.