Ex-Republic of Ireland international Keane has criticised the displays of Rose and Manchester United centre-back Jones, claiming that neither player can properly defend.
"They have to defend better. The two goals they gave away, the one the other night [against Croatia], we see Rose doing that every week and Jones as well," he told ITV Sport. "You defend like that and it's very hard to win games of football against good teams. Everyone gives everything but the two goals they gave away were really poor."
In response, fellow pundit Gary Neville interjected: "The goal that cost us the other night or the one today that Jones gave away and Rose at the back post, we've seen it too many times and they have to rid themselves of these errors."
Keane stood by his initial view, though, adding: "But these players won't Gary, if you make the same mistakes every week it's going to continue, it's not going to change, Jones and Rose, they're not good at defending, they're not good defenders.
"They're working with great coaches, if their coaches aren't going to change them they're going to cost you big style."
England conceded eight goals in their seven World Cup matches, keeping just one clean sheet.