Roberto Martinez's side face Everton on Saturday in the quarter-final of the cup competition knowing they are just 90 minutes from a last-four trip to Wembley.
However, Wigan's place in the top flight is an equally pressing concern, as they are just outside of the relegation zone and level on points with third-bottom Aston Villa, with each of their remaining nine league games now looking like must-win fixtures.
Despite this, Gomez thinks Premier League survival and cup success are both within their grasp.
"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 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."