Rooney came in for some criticism after his performance in the Three Lions' 2-1 defeat to Italy in the Group D opener on Sunday, with Hodgson electing to field the 28-year-old on the flank.
However, the England boss is confident that the Manchester United ace will ignore his detractors and shine for his nation before their tournament comes to an end.
"He came into this tournament wanting to do very well and I think he will do very well in the tournament," the England manager told BBC Sport.
"Wayne has got broad shoulders. He's getting a lot of support from everyone around him. We've got a very clear perspective as to what Wayne is and what Wayne can do. We're hoping for big things from him."