England were bidding to reach a first World Cup final for 52 years but saw their hopes ended by Mario Mandzukic's 109th-minute goal.
At full-time, Keane made his thoughts on Manchester City defender Stone's decision making clear.
On ITV, Keane said: "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.
"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."
Gary Neville added: "Stones has switched off for that goal and he'll know he's made a mistake and he'll have to carry that with him."