Defeats to Italy and Uruguay, coupled with the Azzurri's defeat to Costa Rica, mean Roy Hodgson’s side are unable to progress from the group stages of the World Cup for the first time since 1958.
But Manchester United striker Rooney is determined to take something from a disappointing tournament when they play their final Group D game in Belo Horizonte on Tuesday.
“We are obviously really hurting and disappointed to be out of the tournament. We need to pick ourselves up for this game on Tuesday and go out fighting and showing our pride,” he said.
“It’s not a great feeling to go out of a tournament after two games so we have to try and restore some of our pride.”
Rooney scored his first World Cup goal in the 2-1 defeat to Uruguay on Thursday but he insists it means nothing in the context of failure for the team as a whole.
“I think me not scoring has been on a lot of other people’s minds more than it has my own,” he added.
“I scored a goal but we lost a game and are out of the tournament.
“This team is much bigger than Wayne Rooney is. It is not about me scoring, it is about us doing the right things.
“We were positive but we lost the two games. We have to assess that and try and improve. I am sure we will.”
Rooney also rejected the idea that failure to advance to the knockout stages of the competition would affect his desire to play for his country in the future.
"I am really proud to play for my country," he said. "I never want to pull out of squads, I always turn up and play for England when I am called upon.
"I have no desire whatsoever to stop doing that unless I am told to. I will play for England until I am not selected."
England goalkeeper Joe Hart has already come to the defence of under-fire manager Roy Hodgson and he was keen to reiterate his support ahead of the Costa Rica game.
“We have got to stick together, we have come to this as a group,” he said. “We were looking to succeed as a group but we haven’t.
“We prepared as best we could and just haven’t performed on the field.
“It’s hard to analyse because we have done some good things in this World Cup but we haven’t won the games.
“It’s really hard to take and we are frustrated, it’s an empty feeling right now but we have another game to restore pride and try and get something out of this trip.
“We owe it to the amazing fans who have travelled to come and support us. We also owe it to ourselves as proud Englishmen.
“We are here to do a job, we have not done that, but we’ve got one more game to go. Whenever you play, you play to win.”
Rooney was also keen to defend Hodgson and praised him for improving the England team during his tenure.
"Make no doubt about it, Roy is the man to take us forward. We appreciate what he has done for us,” he added.
"He has, in my opinion, changed the way we have played over the last couple of years and I know the results have been disappointing in the last two games, but as a team we can feel we are getting better.
"I feel with the young lads in the squad, this will help them and hopefully in the future this will make us a better team."