Gordon Smart, who is the editor of the Scottish Sun, broke the story that Hodgson urged Chris Smalling to pass the ball to Andros Townsend using the term "feed the monkey" during the half-time interval of Tuesday's match against Poland.
Smart insisted that he did not think Hodgson meant the comment in a racist way, but also revealed that a number of the players were unhappy with the joke.
"The following morning [after the Poland game] I got call from an England player who wasn't very happy at all about what had gone on in the dressing room. I said to the player, 'Do you think this is a good idea to go public? Is there not another way for you to go through with this? Should you not go to the FA about this? Have you spoken to Roy?' He said no, he wanted to go public and that he wasn't the only player who was upset. They had agreed they wanted to go public with is," Smart told BBC Radio 5 Live.
"I called it in to the office and during the day more than one player did corroborate that Roy had made this remark, that it was taken the wrong way. Across the board everyone did agree it was taken the wrong way. I don't for one second think Roy Hodgson is racist. I just think he chose his words really unwisely and misjudged the room.
"As I understood it, it was Roy speaking to Chris Smalling and telling him not to muck about with it and to feed the monkey. There were a few extra words in there that I can't repeat at this time of day on the radio. It was taken the wrong way and I know that one senior player and Gary Neville looked at each other and at that point said to Roy: 'I think you better explain what you have just said there'. That was when he explained the NASA anecdote."
The controversy has caused the Society for Black Lawyers to call for Hodgson to take part in race appreciation training.