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Rooney, who scored his first World Cup finals goal in the 2-1 defeat against Uruguay that meant England's hopes were over with a group game still to play, said they needed to "be more streetwise."
"Look at teams who have won the tournament in previous years and you can see that nastiness in them," he told a news conference. "A lot of the great teams have that.
"We need to get that in us. We need to be more streetwise. Maybe we're too honest as a team, but I think that will come.
"Uruguay the other night stopped the game. They committed I don't know how many fouls -- clever fouls, really -- to slow the game down. I got kicked 10 times and I don't think there was a yellow card. We try and be honest... maybe that's a fault of ours.
"It's small margins, but those small things can amount to a big thing in terms of staying in the competition or going out."
England face Costa Rica, the team that ended their faint and improbable mathematical hopes with a 1-0 win over Italy, in their final game in Brazil.
Rooney, who has apologised to fans for England's exit, said it would be "a long few days" for the squad as they waited for the meaningless match, but stressed that they would have to gather their spirits.
"It's very disappointing to be out of the tournament," he said. "It's tough, and it's not a great feeling to go out after two games. But we have to try and pick ourselves up for this game on Tuesday and try and restore some of our pride."
Asked whether scoring his first World Cup finals goal had been any consolation for England's dismal showing, he added: "No, not at all. Scoring at a World Cup was on a lot of other people's minds, more than it was my own.
"I scored a goal but we lost the game and went out of the tournament. This team is much bigger than Wayne Rooney. I'm part of this team, and working hard to help it be successful.
"We did a lot of things right and we were very positive -- but in the end we lost the two games."
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