Hull face Brighton tonight for a place in the quarterfinals.
"Obviously whenever you play you want to progress to the next stage, especially when you're in sight of a quarter-final," Bruce Jr said.
"The league is the most important thing but to have a chance of going to Wembley would be massive, the kind of thing you work hard for all your life.
"If we can stay up and do well in the cup that is the perfect situation. Teams take confidence out of winning football matches, regardless of if they are in the league or the cup.
"A win on Monday brings something you can take into the next league game, because it's about playing well and developing that winning habit."