A letter of complaint from a pressure group has been sent to the Football Association demanding that England boss Roy Hodgson attend a “race appreciation” training course after details of his “monkey” joke were made public.

Peter Herbert, the head of the Society of Black Lawyers who also runs the new Race For Sport organisation, sent a four-page letter of complaint to the FA, saying the organisation was wrong to declare the matter closed.

Hodgson, who apologised if any offence was caused, 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 the joke he told in the dressing room at half-time against Poland.

The FA was quick to give Hodgson its full backing over the joke about a monkey in space, which it is believed he used to illustrate why his players should give the ball to winger Andros Townsend.

The letter from Herbert to FA chairman Greg Dyke states that “to announce that the matter is ‘closed’ without any action being taken against the England manager is unacceptable and wholly inconsistent with your policies on equality and diversity.

“For Mr Hodgson or anyone else to make an apology if they fail to understand why the words used were offensive or potentially so is not the response of an institution with the resources and profile of the FA.

“The ‘innocent remark’ made out of ignorance is sadly a common feature of football. We are using the appropriate complaints procedure to urge the FA to provide mandatory ‘race appreciation’ training and ‘cultural capital and cultural intelligence’ training to Roy Hodgson and all football managers in the UK.”

Townsend again played down the incident on Friday, saying that there is no problem between him and the England manager. The Tottenham winger told BBC Sport: “It has all been said now, it has been in the news the last few days and I think everyone should focus on us qualifying for Brazil and not focusing on negative, silly news.

“The manager told the player to give the ball to me, so that is a compliment in a way.”

Several big-name managers have offered their backing to Hodgson, including QPR’s Harry Redknapp.

Redknapp said: “Roy Hodgson is a great guy and he’s certainly not a racist, not a chance.”