The Tigers were widely tipped to be relegated from the Premier League at the start of the season, but have impressed since their promotion from the Championship with a number of good performances, including a 3-1 win over Liverpool on Sunday.
"We knew from the start of the season we'd be underdogs," Bruce told the press. "We were favourites in many people's eyes to go down and that's quite normal for any team coming up from the Championship.
"The one thing we've done is be consistent and played to a level that's given us a chance. That means we've got to play well week in and week out, which is always difficult because you can't afford many off days. We certainly can't have one at Arsenal.
"We'll have to be at our best but we've proved at Tottenham, Everton, Newcastle, Chelsea and Manchester City that we can make a fist of it. We've maybe not got the right result but that's the way we've got to approach it. Let's have a go and see what we can do."
You can read live coverage of Arsenal vs. Hull from the Emirates Stadium with Sports Mole from 6.45pm tonight.