Saturday's victory over Millwall booked a return date at Wembley on May 11th, when Manchester City will stand between Wigan and a first major trophy.
But Roberto Martinez's side remain in trouble in the Premier League, and have seven games to bridge a three-point gap to safety.
"We will do it," said Al Habsi, part of the side which survived on the final day in 2011 and won seven of their final nine games to survive last season.
"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 okay.
"We are a small club and we don't have that many fans but they all believe in the team. To reach the FA Cup final for the first time is amazing.
"But I can promise it won't be a distraction. It all has to be done in order, first the league, then the final, then Europe. Brilliant."