They all failed as a team, from the goalkeeper to the striker. Don't see how only Rooney is at fault, or only Kane.
If there is one individual, who should take most of the blame, that is Roy Hodgson. He looked absolutely hopeless against Iceland, had no idea what to change in order to turn the game around. Not starting Vardy is also criminal, especially after the group stages. His movement would have created so much more space for the midfielders, who were under constant pressure in the last game. Dier was overkill in a match, where England should be dominating heavily. And don't get me started on the set pieces...
Overall, the tactics were abysmal and the team mentality was missing - these are always the causes for England's early exit in every international tournament.