“Obviously we’re hurting,” the Manchester United striker told a press conference at England’s Rio de Janeiro training base.
“It’s really disappointing to be out of the tournament, so I’m sure you can imagine it’s quite tough.
“There’ll be a long few days for us now and we have to try and pick ourselves up for this game on Tuesday, go out fighting and show our pride.”
England lost their first two Group D games 2-1 against Italy and Uruguay and were eliminated on Friday after the Italians lost 1-0 to Costa Rica in Recife.
It is the first time England have gone out in the first phase of a World Cup since the 1958 tournament in Sweden.
Football Association chairman Greg Dyke has confirmed that England manager Roy Hodgson will stay on until the 2016 European Championship and goalkeeper Joe Hart said the squad were fully behind him.
Asked if Hodgson retained the players’ full support, the Manchester City goalkeeper replied: “Of course he does. We’ve got to stick together.
“We came as a group and we tried to succeed as a group. We didn’t, but we’ve got to stick together. We prepared as best as we could have and we just haven’t performed on the field.”
Rooney added: “Make no doubt about it — Roy is the man to take this team forward.”
Earlier, Rooney issued a public apology to England’s fans on his official Facebook page.
“Sorry to all the fans that travelled and at home that we haven’t done better,” said Rooney, who did manage to get his first World Cup finals goal in the Uruguay game.
“Going into each game we had great belief in ourselves, but unfortunately it hasn’t worked out.”
Midfielder Jack Wilshere sent the same message to England’s supporters.
“Gutted doesn’t come close to how I am feeling right now. Sorry to all the fans who came out and supported us, and everyone back home,” the 22-year-old Arsenal player said on his Twitter account.
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