Rooney, 28, has been questioned leading into the FIFA World Cup as his form and ability to perform on the biggest stage comes under the spotlight.
Hodgson is bemused by all the attention surrounding the Manchester United striker and said he just expected Rooney to play his role.
"It is a bit sad that the country is so Wayne Rooney-obsessed," he said.
"I don't think Wayne sets himself up to be anything other than a very important member of the squad, someone who does his best and tries his best at all times.
"Talk about combinations doesn’t interest me. All I want is for Wayne Rooney to play well and Daniel Sturridge to play well.
"We don’t share this obsession with Wayne, we also think that people like Danny Welbeck, Sturridge, Raheem Sterling, Ross Barkley and Adam Lallana are in there to play well and help us score goals, too.
"That's what a squad is about."
Another of Hodgson's strikers, Rickie Lambert, appears close to finalising a move from Southampton to Liverpool.
Hodgson said he had noticed a 'very happy' Lambert, congratulating Liverpool and the 32-year-old on the move.
"I congratulate him. And I congratulate Liverpool signing a good player," Hodgson said.
"When he plays you will see a fella running around with all the joy that his heart can muster because he is very happy to be with England and he's very happy that the move to Liverpool has gone through."
