Dyke was among a number of public figures who condemned Scudamore for the contents of the emails after they were leaked to a Sunday newspaper on May 11.
The Premier League confirmed on Monday that Scudamore, 54, will not be punished for the incident.
"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," Dyke said in an official statement. "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, it was 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.
"This morning Peter McCormick, the acting chairman of the Premier League, came to see me at Wembley to explain the process by which the league has investigated the whole matter and how it reached the decision it made yesterday afternoon.
"He assured me they had followed proper process under their own employment and disciplinary rules and had conducted a thorough investigation."
Scudamore's former PA, who leaked the emails, claimed on Tuesday that she was disappointed by the Premier League's reaction to the incident.