Hull booked a meeting with the Gunners on May 17 after beating Sheffield United 5-3 in an eight-goal thriller at Wembley this afternoon.
Arsene Wenger's men are without a trophy in nine years, and Bruce says that all the pressure will be on the North Londoners to end their barren spell in the showpiece next month.
He told reporters: "The pressure is on Arsenal. They haven't won anything for a while and that will be brought up again.
"We are absolutely delighted. We needed one hell of a turnaround but the one thing you can't do with this team is write them off."
However, Bruce elected to switch to 4-4-2 with the introduction of Matty Fryatt - who scored the equaliser after the break - and the City boss says that altering his formation proved key.
He added: "You have to give credit to Sheffield United. They took care of the ball better than we did and we had a poor first half.
"We needed to go two up top and once we did that we have won out OK."
Tom Huddlestone and Stephen Quinn helped the Premier League outfit into a 4-2 lead, before Jamie Murphy struck in stoppage time to set up a nervy finale to the contest.
However, David Meyler killed off the encounter once and for all in the dying embers to put the result beyond doubt.