Ayew left his struggling side in the lurch and close to relegation when he was dismissed for a vicious elbow on Aaron Cresswell after just 17 minutes in the English Premier League match.
Rock-bottom Villa were actually well on top, having forced a couple of corners and seen a reasonable penalty shout turned down when Gabriel Agbonlahor's cross hit Antonio's arm.
So it was utterly mystifying when Ayew, who was jostling for position with Cresswell from a throw-in deep in West Ham territory, swung his elbow into the defender's face and left him sprawled on the floor.
Referee Jonathan Moss produced a straight red card and Ayew trudged off to leave his teammates facing a long evening with a man down.
Garde was evasive about what action he would take against the Ghanaian striker, insisting he would handle the player in private.
"I will only answer one question on Jordan. It will remain private between him and me.
"I'm not going to speak any more about this incident. I don't need to express any more of my feelings. You can guess Jordan's feelings.
"We have just played 90 minutes of football and I'd like to talk just about the game. Everything that happens in the dressing room of a professional football team should stay there as much as possible."