Albion travel to Championship side Middlesbrough for a fourth-round tie on Saturday before facing important top-flight fixtures against fellow strugglers Southampton, West Ham, Stoke and Swansea.
Manager Hughton has seen his 16th-placed Seagulls win just one of their last 13 league games to slide perilously close to the bottom three.
Just six points separate bottom club Swansea and Watford in 10th and while Hughton wants to progress in the cup, he admits it is difficult not to have an eye on upcoming matches.
Asked if the Premier League games were on his mind, Hughton replied: "Probably to a degree, yes, because we know how important they are, particularly in the position that we are.
"But you can't look too far ahead because if you do then you take your eye off what is important.
"What we want to be able to do is be in this next round of the FA Cup and we know, even from our last experiences in this competition, beating Crystal Palace (in the third round), there's a better feel after the game going into the next league game if you win a game than if you don't, so at the moment all of our focuses are very much on this game."