Hodgson has expressed his frustration and anger that his side's achievement in reaching the World Cup earlier this week has been overshadowed by the details of a joke he told the dressing room in the qualifier against Poland.
Roy Hodgson: "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 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."
Lord Ouseley, chairman of Kick It Out, had initially called for the FA to investigate but the anti-racism campaign group accepted the matter was now concluded following a statement from FA chairman Greg Dyke that confirmed no complaint had been made and none of the players was unhappy with Hodgson's words.
Andros Townsend said 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!"