Goals from Lewis Grabban and Marc Pugh, either side of Lowe's red card for a wild lunge on Tommy Elphick, plus Harry Arter's late stunner, handed the Cherries their third straight win.
And an angry Robinson admitted Lowe will be disciplined for his "idiotic" contribution to the Dons' fourth defeat in six npower League One games.
He said: "He has let everyone down, it's as simple as that. I don't condone it, I don't condone idiotic behaviour.
"We've had it before in the past with Gary MacKenzie and if I think you've shirked something or you've done something against this football club you either take it like a man or you walk away and you're gone.
"Listen, we all have moments of madness, we all do silly things - that was a silly thing and he'll be fined internally.
"But he feels he's let us down, he's apologised publicly and that's all we've got to say on the matter.
"I was disappointed with their players for the way they conducted themselves for large parts of the game.
"The way Elphick grabbed Ryan Lowe round the throat and doesn't get anything done to him and I heard one or two things that were said to him as he was walking off about his wife and his kids.
"We were the better team for large parts of that game, but that one error by Jon Otsemobor and the one by Lowey cost us the game really."