It was reported yesterday that an England player had been offended by a joke that Hodgson told during the half-time interval against Poland about a monkey in space, as the Three Lions boss attempted to show why his team should try to play the ball to winger Andros Townsend.
Townsend and other members of the squad have stated that no offence was taken from the incident, but Hodgson has revealed that it has cast a shadow over his team's achievements.
The former West Bromwich Albion boss told the Daily Mail: "Joy is short-lived in this job. The players are as angry about this as I am.
"We have just had a successful period and, although I wouldn't suggest that we intend to rest on our laurels, I think we have earned the right to enjoy the fruits of our labours. Instead we get this.
"You would have to go a long way to find somebody who is less racist than me. I have coached almost everywhere in the last 37 years, worked with all kinds of people, so this intimation of racism - you can hardly call it a story - is so saddening."
England won the game at Wembley to finish top of Group H.