The England manager was accused of making a racist comment when referring to stand-out winger Andros Townsend.
Hodgson is believed to have told a joke at half-time on Tuesday, where he innocently referred to Townsend as a space monkey.
The joke - originally about NASA, a man and a monkey - was intended to highlight Townsend as an important player for England who should be given the ball more often.
However, some took Hodgson's comments out of context and have claimed the former Fulham boss acted in a racist manner.
Hodgson has spoken to Townsend since and was reassured that the Tottenham winger understood the context of the remark:
"I would like to apologise if any offence has been caused by what I said at half-time," Hodgson is quoted as saying in the Telegraph. "There was absolutely no intention on my part to say anything inappropriate. I made this clear straight away to Andros in the dressing room."
The England chief has also received the backing of star striker Rooney.
The forward - who scored with a header against Poland - has rubbished the story, and supports his national manager.
The United finisher used his Twitter account to give his opinion on the matter, tweeting:
"Seen the story on Roy this morning. He done nothing wrong. This is ridiculous."
66-year-old Hodgson guided to team to the World Cup just days ago, and that the accusation has been rubbished by one of his senior stars will be much appreciated.
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