Allardyce responded angrily to criticism from Gartside in radio interviews before the game.
Gartside now wants to draw a line under their public row.
"I'd like an end to it, because it's not healthy for either of us," he told the Bolton News.
Allardyce is also reported to have been angry his VIP guests, including his son Craig, the former football agent, were denied access to the directors' box.
That is a claim Bolton refute, explaining that they felt it more prudent to accommodate their former manager's guests in two executive boxes.