England were held to a 2-2 draw against Ecuador in Miami on Wednesday, with Wayne Rooney and Rickie Lambert finding the net for Hodgson's men.
Barkley turned in a fine display at the Sun Life Stadium - capped off by his jinking run to set up Lambert's goal - but it seems the Everton midfielder has a way to go to force his way into contention for the England starting XI at the FIFA World Cup in Brazil.
"I'm not prepared to address your (the media's) obsession with Ross Barkley," England boss Hodgson told reporters after the match.
"He lost the ball an awful lot of times as well. If he's going to be the player we want him to be, he has to make better decisions of when he turns with the ball.
"That's not a criticism, but there were other performances out there who merited your 'obsession' more than Ross Barkley's.
"(Alex) Oxlade-Chamberlain and Phil Jones were outstanding, Jack Wilshere in the middle of the park and Rickie Lambert scored a magnificent goal."
There is, of course, no guarantee that Barkley will be given the chance to impress on Saturday in the side's final friendly before the World Cup, with Hodgson likely to field a stronger team against Honduras, having handed opportunities to fringe players on Wednesday.
Hodgson appears likely to be without the services of Oxlade-Chamberlain, who faced a scan on a knee injury on Thursday, while Raheem Sterling is suspended after being sent off for a reckless challenge on Ecuador's Antonio Valencia.
England climbed back into the top 10 of the FIFA World rankings on Thursday - Honduras are 33rd - but that will count for nothing if Hodgson's men are unable to hit their stride heading into the World Cup.
