Pep Guardiola’s side secured their qualification to the Round of 16 in Germany as they came from behind thanks to David Silva’s goal cancelling out Raffael’s opener.
Both sides finished with 10 men after Lars Stindl picked up his second yellow card on 51 minutes, 12 minutes before City midfielder Fernandinho followed suit.
But it was Stones’ defending which riled the Republic of Ireland assistant manager after he was brushed aside too easily by Stindl in the build-up to Raffael’s goal.
The Englishman’s protestations for a free kick were ignored and an unimpressed Keane told Stones he needed to toughen up.
"It's just too easy, he's like a child getting knocked off the ball," Keane told ITV.
"He's hoping one of his team-mates can help him out here but they punished and rightly so. Really poor defending, he's got to be stronger.
"He's a good player but he's just got to be tougher and stronger."
Lee Dixon agreed with Keane and berated Stones for going down too easily and gambling that the referee would award a free kick.
"Where you are on the pitch, you can't take a chance and go down,” said the former Arsenal defender.
"That pull on his arm wasn't enough to send him to the ground.
"He's taken a gamble thinking the ref will see it. If you're last man you can't take a risk like that. You've got to fight him off, get the ball back to the keeper and the danger is gone."Reuse content