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After being named by the Football Association as successor to former England boss Mark Sampson on Tuesday (local time), the 41-year-old Neville attracted criticism for remarks he posted on Twitter in 2012.
"Morning men couple of hours cricket be4 (sic) work sets me up nicely for the day," Neville posted.
Asked why he only referred to men, he replied: "When I said morning men I thought the women would of been busy preparing breakfast/getting kids ready/making the beds - sorry morning women!"
In a letter to 'Kick it Out', football's equality and inclusion organisation, FA chief executive Martin Glenn said the ruling body only learned of Neville's tweets on Tuesday.
He confirmed that Neville, who signed a contract with England until 2021, would be warned about his conduct.
"Phil will be educated on all aspects of the FA's regulatory functions and his responsibilities," Glenn said.
"He will also be warned that any future comments that are deemed to cross the charging threshold will be treated with the utmost seriousness and may lead to disciplinary action.
"The background vetting highlighted some but not all the historic social media comments. For clarity, we were only made aware of some of those comments through the media reporting [on Tuesday]."
Neville, the former England and Manchester United defender, deleted the posts and took down his Twitter account after taking up his new role. He apologised in a statement released by the FA earlier on Wednesday.
"Following comments made a number of years ago I would like to clarify that they were not and are not a true and genuine reflection of either my character or beliefs, and would like to apologise," Neville said.
"I am fully aware of my responsibilities as the England Women's Head Coach and am immensely proud and honoured to have been given the role," he added.
"I am now looking forward to the future and will work tirelessly to try and help bring success to the team."
Glenn's letter came after "Kick It Out" expressed concerns about Neville's appointment in a strongly-worded statement on Wednesday.
"The appointment of Phil Neville as Head Coach of the England Women's Senior Team ultimately raises more questions than answers for The Football Association," Kick It Out CEO Roisin Wood said.
"In light of recent action taken in response to historical social media comments made by current football participants, the question must now be asked – will The FA be charging Neville for posting discriminatory comments on social media?
"We believe that if The FA wants to recover the confidence of the public, it must ensure that the concerns surrounding Phil Neville's appointment are comprehensively addressed."