England have already been eliminated from the tournament, their earliest exit in 56 years, having lost 2-1 to both Italy and Uruguay in their previous two Group D matches and return home after playing Costa Rica on Tuesday in Belo Horizonte.
"You look at teams who have won the tournament over previous years and you can see that nastiness in them," said Rooney who could hardly hide his disappointment when he spoke to the media at the team's training camp. "I think we have to get that in us.
"As a team maybe were are too honest, I feel."
Rooney added he agreed that England needed to get more 'streetwise' in major tournaments in terms of controlling the tempo of games.
"I think so. You see a lot of the great teams, international and club teams, they have that," he said. "The time to slow the game down a bit or control the game a bit more.
"But this is football. You have to take your chances (and) if we'd taken as least one of them, we'd have gone on and won the games. That's what disappointing."
He also felt that Roy Hodgson's side needed to learn the darker arts of committing tactical fouls, something he felt Uruguay had done well and got away with.
"They committed I don't know how many fouls, clever fouls, really, which slowed the game down.
"I got kicked 10 times (against Uruguay) and I don't think there was a yellow card given to an opponent. We try and be honest, but maybe that's a fault.
"It's small margins, but those small things can amount to a big thing in terms of staying in the competition or going out."
Rooney said he would watch the rest of the World Cup on television when he got home, while he had a new favourite to win the tournament.
"Holland," he replied with a straight face when asked who he hoped would win the tournament, a diplomatic reference to the Dutch team's manager Louis van Gaal taking over at Rooney's club Manchester United at the conclusion of the World Cup.
"To be honest, I'm not really fussed," he then added.
"It's a fantastic tournament to be a part of and I'm disappointed to be going out, but I'll watch from home."
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