Mack spoke to reporters on Thursday, addressing the disappointment and anger Bombers fans have been feeling since the team lost 52-0 to the Saskatchewan Roughriders in Sunday's Labour Day Classic in Regina.
"It's not acceptable, but it happens," Mack said, adding that he, too, was surprised by the huge loss.
Mack had been silent earlier this week, while thousands of fans joined the "Fire Joe Mack" movement on Facebook and Twitter to call for his dismissal in light of the team's poor performance this season.
The Bombers' board chairman, Bill Watchorn, said earlier this week that the board has confidence in Mack, despite the growing public backlash.
On Thursday, Mack said he supports the board's decisions and he won't step down as general manager.
"This board will do whatever they think is necessary for the betterment of this club," he said.
Sunday's dramatic loss to the Roughriders brought the Blue and Gold's record this season to 2-7 and prompted fans to question the club's decision on Aug. 25 to fire Paul LaPolice as head coach.
LaPolice was replaced on an interim basis by defensive co-ordinator Tim Burke. Sunday's game was Burke's first CFL game in the head coach position.
But Mack noted that in the past, football teams have come back from such major losses and turned things around.
Some fans have also expressed anger at the club's home-game security measures, banning fans from bringing homemade noisemakers and outside food and drink to the stadium.
At the same time, some fans have said they remain hopeful the Bombers can turn things around when they meet the Roughriders again in this weekend's Banjo Bowl match in Winnipeg.