Boyce is confident Wigan will not take their eye off the ball when it comes to the league and cited the experience of Birmingham, who won the League Cup in 2011 but were relegated.
Ahead of their FA Cup semifinal with Millwall, he said: "You just have to look at Birmingham a couple of years ago. I don't know whether they took their minds off the Premier League, but they got relegated.
"We need to stay in the Premier League, that's the be all and end all. We know how football can change so quickly. We can go into the semi-final on track to have a great finish to the season or it could be a big disappointment."