Thursday's 2-1 defeat at the hands of Uruguay in Sao Paulo left England on the brink of elimination, with their fate confirmed on Friday when Costa Rica beat Italy 1-0 in Group D.
Despite seeing his country go out at the group stage for the first time since 1958, Rooney has given his full support to coach Hodgson, as England begin to set their sights on their UEFA Euro 2016 qualifying campaign.
"No doubt about it, Roy is the man to take us forward," the Manchester United striker told a press conference.
"We appreciate what he has done. In my opinion he has changed the way we play and you can see the progression.
"I know the results have been disappointing but as a team we can feel we're getting better and hopefully this will make us better as a team.
"He's put great enthusiasm into the team and put a great set of young, exciting players in place."
As they come to terms with the bitter disappointment of an early departure from Brazil, Rooney has also called upon the rest of the England squad to use the failure as a motivating factor in the future.
"The young players can come to this tournament and learn from it, we all can," he added.
"It's vital we do that. We have to remember the pain and come the next tournament we have to make sure we don't feel that again."
