The former Manchester United defender has been widely criticised since his appointment last week after comments he made on Twitter a few years ago came to light, one of which said he had "just battered the wife".
In his first interview since taking charge, Neville reiterated an apology he made last week, saying he was wrong to post the remarks on social media in 2011 and 2012.
"That tweet was not sent out in terms of domestic violence but the words were not right then and not right now," said Neville, adding that the reference was to beating his wife at sport on holiday.
"I had to apologise, I didn't like the words used. I'm not a sexist. I've lived my life right," said Neville who has since deleted his Twitter account.
Neville, 41, has also been criticised for his lack of experience of women's football, but he said he had coached extensively at a high level.
"I'm qualified for the job, I have a (coaching) Pro Licence. It's to work in all aspects of football. I've worked abroad. I'm best qualified for this job." said Neville, who has never been a manager but coached at Manchester United, England Under-21s and Spanish side Valencia.
Neville said that just as women were now encouraged to comment on men's football as TV pundits so he should be allowed to enter the women's game without any direct experience.
"The gap (between the men's and women's game) is closing and I would have thought there were not many candidates with my experience of elite players," he said.
Neville's remarks represent an attempt to draw a line under a saga that has split a women's game still recovering from the sacking of previous head coach Mark Sampson for inappropriate behaviour in a previous job.
The English FA had clearly hoped Neville's appointment would begin a new era; instead it plunged the game into further turmoil.
Neville met his new team for the first time at a training camp in Spain last week, stating that his intention was to take the team to the next level.
(Reporting by Neil Robinson, editing by Ed Osmond)
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