Rooney's performances for the national team have been the subject of intense scrutiny since he burst on to the scene as an 18-year-old with four goals at Euro 2004, and he is seen as the key man for England at every major tournament.
But Hodgson thinks the interest in Rooney has become an 'obsession', and was agitated when questioned about the player and how he did not perform as well as his replacement Raheem Sterling, against Peru on Friday.
Hodgson was full of praise for Rooney after the 3-0 victory at Wembley, hailing the 28-year-old's drive, commitment and energy in a briefing for Sunday newspapers.
"I think it's a bit sad that the country is so Wayne Rooney-obsessed," Hodgson said.
"I don't think Wayne sets himself up to be anything other than a very important member of the squad who tries his best at all times.
"We work as a team but certainly we don't have the same obsession with Wayne, or Daniel Sturridge.
"It's a little bit infuriating to see players who have come on in the last 10 or 15 minutes of a game when it's over and there are loads of spaces and the opposition are on their knees compared to players who are on the pitch when opponents are very fit and determined to keep you at bay, throwing themselves into challenges."
Former Manchester United midfielder Paul Scholes questioned whether Hodgson would have the gumption to drop Rooney if the striker, who is yet to score at a World Cup, does not produce the goods.
Interestingly, Hodgson failed to name Rooney as one of his definite starters for England's Group D opener against Italy in Manaus on June 14.
"In the back positions we have a pretty clear idea of what we want," Hodgson said when asked if he knew how his team would line up versus the Azzurri.
"Once you get past Steven Gerrard in midfield, there are five positions to fill.
"I think there are plenty of options there and we could do well with a number of those options."