England were dumped out of the tournament following a surprise 2-1 defeat, while Hodgson announced his resignation in a pre-prepared statement after the match.
Reports which surfaced on Tuesday claimed that England’s senior players had questioned Hodgson’s ability to guide the team through the tournament but Rooney insists the 68-year-old was fully supported by the squad.
“In response to recent media reports, I'd like to say that is completely untrue,” the England captain said in a statement.
“On behalf of the players, we completely supported the England manager but we understand his reasons for stepping down.
“We had absolute faith in the build-up and throughout the tournament.”