FA chairman Greg Dyke met his counterpart at the Premier League, Peter McCormick, on Tuesday for talks over the issue after the top-flight clubs decided to take no action against Scudamore.
One member of the FA's inclusion advisory board (IAB), equality campaigner Edward Lord, has obtained a legal opinion that the FA could take disciplinary action but Dyke reaffirmed that will not take place.
Dyke said in a statement: "Last week, the FA made it clear that Mr Scudamore was not an employee of the Football Association and, as such, we had no position in terms of employment policy or taking disciplinary action.
"We were of the view that was a matter for the Premier League and we asked them to keep us informed of the actions they were taking.
"In terms of wider FA disciplinary action, we were advised that the FA does not as a matter of policy consider private communications sent with a legitimate expectation of privacy to amount to professional misconduct. The FA has applied this policy on an ongoing basis and in relation to numerous other cases."
IAB chair Heather Rabbatts, was also at the meeting with acting chairman McCormick, and she will take on the task of ensuring the Premier League keeps to its " undertaking to take further steps on inclusion and diversity".
Dyke said McCormick has assured him the league had followed "proper process under their own employment and disciplinary rules and had conducted a thorough investigation".
The FA chairman added: "We said last week that we considered the contents of the emails in question to be totally inappropriate and are still of that view, as is the Premier League.
"It is important to reiterate the significant focus the FA gives to equality, not least through the work of its Inclusion Advisory Board (IAB), and to tackling all forms of discrimination.
"FA board member Heather Rabbatts... joined me in this morning's meeting. I have asked her to follow up with the Premier League to discuss the wider issues around the inclusion agenda and see how the FA and Premier League can work together to make meaningful the League's undertaking to take further steps on inclusion and diversity."
Rani Abraham, the former temporary personal assistant who leaked the emails, said she was disappointed and surprised the Premier League had taken no sanctions against Scudamore.
She told BBC Radio Five Live: "I'm highly surprised the Premier League have decided to take no sanctions whatsoever against Richard Scudamore.
"I feel very disappointed, I think it sends out a damaging message about how we regard women in football."
Abraham said she had not been contacted as part of the league's investigation.
She added: "They haven't approached me, they haven't heard my side of the story so there has not been a thorough investigation. I honestly think they are not taking the sexism seriously."
Abraham said that she had been threatened with legal action by the Premier League after taking the emails to the Sunday Mirror and was herself now considering taking legal action against the organisation.
She added: "When I approached the Mirror I received a letter from the Premier League's lawyers threatening legal action. They said there had been a breach of trust, it was a very threatening letter, I have had a couple now, and I believe the Premier League are trying to scare me.
"I won't go quiet because I am standing up for what I believe in.
"I haven't taken legal action but I am speaking to a solicitor at the moment."
The Premier League would not comment on Abraham's latest claims. It is understood however that she was asked to return the copies of the emails she had taken as they contained confidential and commercially sensitive information, and that the contents of the emails should be treated as confidential.
Scudamore spoke of his "sincere contrition" after the top-flight clubs decided against any disciplinary action against him and vowed to hold a series of meetings across football's administration to reassure them of his commitment to promote women in the game.
- Sports & Recreation
- Premier League