Less than four minutes into England's third-place playoff with Belgium, Thomas Meunier was able to slip in behind Rose, to turn in Nacer Chadli's cross.
Rose was substituted at half-time after a generally poor first 45 minutes.
Belgium's second goal puts Jones at fault, as he was unable to stop Eden Hazard from a run on goal.
Roy Keane gave a particularly honest review of the defending that led to the goals.
The United legend said on ITV following the game:
"If you’re making the same mistakes every week, it’s going to continue. They are not going to change. Rose and Jones."
"Because they are just not good at defending, they are not good defenders… They are working with some great coaches. If their coaches aren’t going to change them, they are going to keep doing it and they are going to cost you big style."
"England obviously gave a shocking goal away," he said at half time. "Sloppy, lazy defending... Really lazy defending."
"When you look at Rose's defending as well on top of the centre-halves (Jones, John Stones and Harry Maguire), he's never going to learn about the game if he doesn't know that at 28 years of age. He's in trouble."
Fellow ITV pundit Lee Dixon also laid a lot of the blame at Jones' feet, after the defender drifted out of position in pursuit of Hazard.
"It was early in the game. We looked tired, we looked sloppy,' Dixon said. 'Roy's right, some of the defending that went on was really poor."
"Jones goes into midfield, following Hazard. When Jones goes in, just watch, he just wanders in. That leaves us short now in the middle so they can't go tight."
"Two centre-backs drop off, (Romelu) Lukaku feeds it inside. We've got a four v two there, how we get beat... we've got to block the near post off, block the cross from coming to the far post. We do neither and that's a really poor start."