The 20-year-old was handed his first international start in Miami and marked it with an assist as he ran from the halfway line before passing to Rickie Lambert, who in turn drove the ball into the bottom corner.
But Hodgson believes that there is a slight obsession with Barkley given his age and instead looked to praise other performances, including those of Phil Jones and Jack Wilshere.
"There always seems to be an enormous obsession with one player," he told reporters.
"I will be prepared to start any of the players in any game but I'm not prepared to address your obsession with Ross Barkley.
"If he's going to be the player we want him to be, he has to make better decisions when he turns with the ball.
"That's not a criticism but there were other performances out there today. [Alex] Oxlade-Chamberlain and Phil Jones were outstanding, as was Jack Wilshere in the middle of the park, while Rickie Lambert scored a magnificent goal."
England's World Cup preparations continue as they take on Honduras on Saturday before flying to Brazil ahead of their opening Group D match against Italy on June 14.