Stones switched off to allow Mandzukic time and space inside the England box, and Keane has accused the Manchester City centre-back of 'not smelling the danger'.
"We've talked about how comfortable England are playing out from the back and that it's in their DNA and Stones is comfortable on the ball you still have the act of defending. Players smelling danger," Keane told ITV.
"Stones is ball watching and then when the goal goes in he's looking at people as if he should have got a shout. You're not going to get a shout in a World Cup semi-final.
"You've got to be aware of it and deal with it yourself. He does get caught out defensively."
England will now take on Belgium in the third-place playoff match on Saturday afternoon.