The Three Lions have been eliminated after losing their first two matches of the tournament against Italy and Uruguay, meaning they failed to progress to the knockout stages for the first time since 1958.
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"Roy has brought in an enthusiasm to the squad, and introduced youngsters. Make no mistake - he is the man to take us forward,” Rooney said on Saturday.
"We appreciate what he's done for us. He's changed the way we play over the last couple of years. You can see the progression.
“I feel we're getting better and this will help the younger players and help us become a better team.
“We're hurting, disappointed to be out of the tournament but we have to pick ourselves up for Tuesday [against Costa Rica] and restore some pride
“We have to learn from this, we need to be more clinical and take our chances.”
In a sombre press conference at England’s training base in Urca, goalkeeper Joe Hart apologised to the supporters for the team’s failure to reach the second round.
Hart said: “We'd like to thank fans for making the difficult journey to Brazil. The sacrifices they made. We can only apologise.
"It's a really strange, empty feeling. This is ultimately really cruel. It's gutting for me."