Moyes, who signed a four-year contract when he replaced Sam Allardyce, guided Everton to a top-six league finish four times and built his reputation on getting the most out of a limited squad.
"It's been a turbulent start," Bain, who replaced Margaret Byrne as chief executive earlier this year, told the club's website.
"David is an experienced manager and he is a character. I think he is in the top four most experienced managers in the Premier League in terms of games managed. Fundamentally, that experience, coupled with David's longer term approach.
"He is a builder. He understands the need to win, first and foremost, but in parallel, he understands that the job he has come here to do -- and the job I have come here to do -- is to build, to rebuild really."
Sunderland have flirted with relegation for the past four seasons, with Moyes being the fourth full-time managerial appointment since they sacked Paolo Di Canio in September 2013.
"We can certainly change the future. From both our perspectives it's about rebuilding, let's do the basics right. That's the biggest message I want to get across, we want to get back to basics," Bain added.
Striker Jermain Defoe, who racked up 15 league goals last season to help Sunderland avoid relegation, believes the club had "gone backwards" following Allardyce's departure.
"We're coming into November and you don't want to be getting into a situation at the bottom of the league like we have every year," Defoe said.
"From where we were towards the end of last season, I feel like we've gone backwards a little bit. I don't know why, I can't put a finger on it. We've not hit the levels that we reached towards the end of last season."
Sunderland travel to West Ham United for a Premier League encounter on Saturday.
(Reporting by Ian Rodricks in Bengaluru)
