The 66-year-old told a joke about "space monkeys" and NASA in an attempt to press upon his players to pass to the impressive Andros Townsend, a story which at least one player allegedly believed had racist connotations.
The Tottenham winger himself insisted he had not been at all offended by the comment, and Rooney has also taken to Twitter to express his shock at the way the incident has been reported.
"Seen the story on Roy this morning," Rooney wrote. "He [has] done nothing wrong. This is ridiculous."
Hodgson quickly apologised for his words but insisted that there was no misunderstanding of meaning between him and Townsend.
I don't know what all this fuss is about. No offence was meant and none was taken! It's not even news worthy!— andros townsend (@andros_townsend) October 17, 2013
"I would like to apologise if any offence has been caused by what I said at half-time," he stated.
"There was absolutely no intention on my part to say anything inappropriate. I made this clear straight away to Andros in the dressing room.
"I also spoke to Andros again on Wednesday. He has assured me and the FA he did not take any offence and understood the point I was making in the manner I intended."