Neville was officially unveiled at his new club on Tuesday but faced some difficult questions from reporters regarding his history of sexist tweets.
The former Inter Miami and Lionesses boss admits his tweets were "wrong" and said they do not reflect his true values.
"The big part of this city is the supporters, and the statement they put out showed that this club cares about their people," Neville explained.
"In reference to the tweets I made in 2011, I addressed these in 2019 when I was named the head coach of the England women’s team. (They are) by no means a reflection of me as a person, of my character, and without a shadow of a doubt, the way I was brought up by my mother and father in terms of the values they instilled in me.
"The tweets I put out were wrong in 2011, and they’re wrong today. I want to get to know the Timbers Army, I want to get to know everybody in the city, and I want them to get to know me as a person, as a character. And I want to make sure there is an incredible trust between us."
Neville previously apologised for his tweets back in 2018 after being appointed manager of the England women's team, after users pointed out his posts which have since been deleted.
One tweet read : "Relax I'm back chilled - just battered the wife!!! Feel better now!" Another posted by Neville said: "U women of [sic] always wanted equality until it comes to paying the bills #hypocrites."
Neville's appointment had been criticised by the Portland fan group 'The Timbers Army' on Instagram.
"We are deeply disappointed that the club has reportedly settled on a finalist for head coach who has a history of sexist public statements that run counter to our ethos as a club, city and supporters' group, and who also lacks a proven track record as a manager," read a statement from the fan group.
Portland general manager Ned Grabavoy was also asked about his decision to appoint Neville, and backed him as the right man for the job. Grabavoy added that Neville's sexist tweets are "not indicative of his character."