Hodgson's decision to tell a joke about a monkey and an astronaut during half-time of Tuesday's World Cup qualifier against Poland has been the subject of much debate.
Kick It Out and Peter Herbert's Race for Sport had both asked for an investigation but the FA gave their "full support" to Hodgson after looking into the issue and Kick it Out say they now consider the matter concluded.
A Kick It Out statement read: "We are pleased that the Football Association has investigated this matter swiftly and issued its findings immediately.
"If there has been no complaint on the back of the investigation then the matter can only be deemed as concluded.
"Kick It Out acts on behalf of the football community at large and when an allegation of a racist or discriminatory nature is made, it's the organisation's role to follow this up."
The player who was the subject of the joke, Andros Townsend, was one of the first who took to Twitter to downplay the saga.
As the furore surrounding the controversy gained momentum, FA chairman Greg Dyke released a statement on the FA's website offering his "full support" to the manager.
"Roy Hodgson is a man of the highest integrity, an honourable man who is doing a great job with the England team," he said.
Dyke added: "He has fully explained to us what he said and the point he was making to the players in the dressing room at half-time 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 apologised for any unintended offence 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."
Wayne Rooney also took to Twitter to back the manager:
Dyke went on to make clear in his statement that despite a player's apparent dissatisfaction with the joke as reported in two tabloids, they had received no complaint through their official channels.
"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.