The Three Lions were eliminated from the competition at the group stage on Friday following Costa Rica's shock victory over Italy.
While the team has nothing to play for in Belo Horizonte next week, Rooney believes that a win would at least give them some reward for their efforts out in Brazil.
"We're hurting, disappointed to be out of the tournament but we have to pick ourselves up for Tuesday and restore some pride," he told reporters.
"It's tough to take and it's the first time we have gone out of a tournament after two games. We have to pick ourselves up."
Rooney scored his first ever World Cup goal for England on Thursday during their 2-1 defeat to Uruguay.