Latics are out of the relegation zone only on goal difference with 10 matches remaining, but switch their attentions to the FA Cup this weekend and a quarter-final tie at Everton.
"We have two objectives for the rest of the season, but I believe we can achieve both," Gomez told the Wigan Evening Post.
"After the Everton game, we have 10 matches left in the league and we will need to improve our performances to stay in the division.
"But we have been here before and we have always managed to get out of trouble, so I think we can do the same and remain in the Premier League.
"As far as the cup is concerned, we are only two games away from the final, and we are determined to keep going in both competitions for as long as possible.
"It's never boring at Wigan - we are always fighting for something and we won't stop until the end of the season."