FA chairman Greg Dyke has issued a statement expressing support for the England manager, whose comments during halftime of Tuesday's match against Poland provoked controversy.
Hodgson is said to have used an analogy comparing right back Chris Smalling's role in passing the ball to winger Andros Townsend to that of a NASA astronaut who was charged purely with feeding the monkey while on a mission into space.
While Townsend himself insisted via Twitter that no offense was taken, chairman of anti-racism group Kick It Out Lord Herman Ousley had urged the FA to investigate the comments.
“Roy Hodgson is a man of the highest integrity, an honorable man who is doing a great job with the England team. He has and deserves the full support of The Football Association," Dyke said in a statement. “He has fully explained to us what he said and the point he was making to the players in the dressing room at halftime on Tuesday night. He has also explained the context in which he made his remarks.
“He has made clear there was no intent to say anything inappropriate, and he was certainly not making any comments with any racist connotation. Importantly, he has apologized for any unintended offense that may have been taken.
“Roy has spoken with Andros Townsend and a number of the players since the game and he has been assured there are no problems within the squad whatsoever.
“Additionally The FA has not had a complaint from any squad member or player representative, and we have today talked extensively to the squad. The FA has been assured by the players that there are no problems and they understand the point Roy was making and the context in which he was speaking.
“We will be making no further comment on this story and will now be giving Roy and the team our full support as we prepare for the World Cup in Brazil."