The Football Association is facing new questions about a potential cover-up after announcing Lee Kendall, England Women’s goalkeeping coach, would not face action over allegations he spoke to Eni Aluko in a mock Caribbean accent and releasing a statement to “wish him well for the future” while concealing the fact he had admitted her accusations were true.

Kendall resigned from his position on Thursday despite a statement from the FA saying its four-week investigation into his conduct, sparked by Aluko’s evidence in a parliamentary hearing into the Mark Sampson affair, had “decided that no further action was necessary”.

What that statement did not mention, the Guardian can reveal, was that Kendall had admitted to putting on a Caribbean accent and making a number of comments to Aluko in keeping with her submissions last month to the digital, culture, media and sport select committee that it was another “example of an ignorant mindset and behaviour towards me”. Aluko, whose complaints about Sampson eventually led to a full apology from the FA, had said she did not believe Kendall was being malicious or deliberately offensive but highlighted his conduct to demonstrate the ignorance she had to endure in the England setup.

Kendall’s admission leaves questions about why the FA, already accused of putting together a “sham” inquiry to clear Sampson, would state publicly it felt no action was necessary – a line it has now accepted was untrue – and then released a statement that appeared to exonerate the goalkeeping coach.

“The FA has completed its investigation into allegations made by Eniola Aluko regarding Lee Kendall and it was decided that no further action was necessary,” the statement read. “Despite the FA’s conclusion, Lee Kendall has decided to resign from his position as goalkeeping coach of the England Women’s senior team. It is Lee’s choice to focus on the future and on pursuing his career elsewhere. We wish him well for the future.”

The Guardian has asked the FA for an explanation as to how Kendall could be under investigation for speaking to a black player that way, and admit it was true, only for the organisation to release a statement that made it appear as though he had been cleared of any wrongdoing. The governing body declined to comment on the record but confirmed that Kendall had accepted the allegations were true. The organisation also admitted, contrary to its own statement, that it did deem action to be necessary and that Kendall would have been required to take diversity training if he had remained in its employment.

No explanation was offered as to why this was left out of the statement or why it was worded to make it seem as though he had been exonerated. The FA did not respond to the question about whether it was a deliberate attempt to cover up the fact that one of its coaches had, as alleged, repeatedly made a black player feel uncomfortable by speaking to her in a fake accent.

The latest development also raises new questions about Sampson’s version of events bearing in mind the now-deposed England Women’s manager was asked, in an interview with Sky Sports on 6 September, whether a member of his staff had spoken to Aluko that way and said he had checked with all his coaches. “There was no evidence found of that taking place,” he said. “I stand by my staff, I’ve spoken to all my staff. The intention of all my staff in regards their communication is exactly the same as mine – to support these players and help be as successful as possible for their country.”

Sampson also pointed out that it had formed part of the independent inquiry, led by the barrister Katharine Newton, that had to be started again because of the huge amount of criticism attached to her findings, having initially cleared him of any wrongdoing. Newton’s revised findings concluded that he did, in fact, ask Drew Spence, a mixed-race player, how many times she had been arrested and that Sampson also told Aluko to be careful her Nigerian relatives did not bring Ebola to Wembley. Sampson was subsequently sacked because of an old safeguarding investigation.

Newton’s verdict led to an official apology from the FA and widespread calls for the chairman, Greg Clarke, and the chief executive, Martin Glenn, to consider their positions amid a series of highly damaging revelations about an internal review described by the Professional Footballers’ Association as “not a genuine search for the truth”, featuring “incontrovertible evidence that makes it clear the purported investigation was a sham”.

Both men have clung on their jobs, as have the technical director, Dan Ashworth, and the director of human resources, Rachel Brace, the two executives in charge of the internal inquiry. Ashworth had admitted at one point supplying 16 names to Newton as potential witnesses for the Spence case but not including Spence herself or any of the other six people who were present at the time. He also gave Sampson a character reference, at an inquiry he was leading.

What has been widely unreported is that the FA was first made aware last November, via a letter from the PFA, about a member of Sampson’s staff speaking to Aluko in a Caribbean accent. Hence Aluko informed the FA last month she did not wish to take part in an investigation she felt should have taken place almost a year ago.

Aluko had already accepted an apology from Kendall over an unrelated incident, when he was overheard making unpleasant remarks about her, and wanted to draw a line under the whole affair. Kendall has apologised to the FA for the events that led to the latest investigation.