The 66-year-old told a joke about "space monkeys" and NASA in an attempt to urge his players to pass to the impressive Andros Townsend, a story which at least one player allegedly believed had racist connotations.
But the Tottenham has since come out to defend his manager on Twitter: "I don't know what all this fuss is about. No offence was meant and none was taken! It's not even news worthy!" he said.
Rooney did likewise, expressing his shock at the report: "Seen the story on Roy this morning. He [has] done nothing wrong. This is ridiculous."
|20/1||Andros Townsend is 20/1 with William Hill to be England's top scorer at World Cup 2014|
"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."