The Latics are three points away from safety, but they reached final of the FA Cup last weekend with a 2-0 win over Millwall.
Wigan play Manchester City on Wednesday night in what is a dress rehearsal of their Wembley showdown next month, but Al-Habsi has insisted that his side are focused on securing their Premier League survival.
The 31-year-old told the Daily Star: "We will do it. We will stay in the Premier League. The FA Cup won't distract us.
"Our squad is big enough to cope. We have been in this situation many times. We believe in ourselves and we will be OK.
"If we win we're happy. This club is like a family. I believe in every single player here, no matter who is starting."
The Oman international has featured on 32 occasions for Wigan this season.