The tabloid received complaints after they made fun of the England manager's inability to roll his 'R's on its front page in May.
FA chairman David Bernstein later described the newspaper's front page as "disrespectful" and "in poor taste".
Editor Dominic Mohan described the FA's criticisms as "perverse" and "ill-considered" after he was asked by the Leveson Inquiry to explain the decision behind the headline.
"The FA is entitled to its opinion, but I regard their criticism that the headline was 'in poor taste and disrespectful' as an ill-considered response, something I told the FA myself at the time of their complaint."
Mohan did however regret The Sun describing Hodgson as having a speech impediment.
"On reflection, I do not regard someone's inability to roll their 'Rs' as a speech impediment," he conceded. "Rather it is a simply a distinguishing feature of their speech."
He also cited four Guardian articles that used the word "Woy" between 2009-2011, and five stories in The Mirror between 2010-2012.
Jonathan Ross - who also has Hodgson's rhotacism speech issue - defended The Sun's frontpage after it was released.