Hull will contest their first Cup final against Arsenal next month, but were beaten 3-0 by Arsene Wenger's men in Sunday's league meeting at the KC Stadium.
Two goals from Lukas Podolski and one from Aaron Ramsey secured Arsenal's win and subjected Hull to a third loss in their last four top-flight matches, keeping them six points above the drop zone with four games to play.
Bruce targeted 10 wins to secure survival in pre-season - which Hull have achieved - but the former Sunderland manager will not look forward to the Cup final until his team's place in the Premier League is mathematically assured.
"I am not interested in Wembley, we've got to stay in this league and let Wembley look after itself," he said.
"We have got to concentrate on the next few games, make sure we get over the line, we haven't done it yet, we're not safe yet and we've still got a bit of work to do, and that's what I'm concentrating on.
"I always said if we get 10 wins that's usually enough, it still might be, but it's too close for comfort.
"We've seen some unbelievable results over the weekend, it's concertinaed and it's quite a remarkable league this year."
Hull started the game well with Ramsey's goal arguably arriving against the run of play, and Bruce also bemoaned what he perceived to be a foul in the build-up for Podolski's first.
"The first half (was the) best we've played for weeks, I couldn't have been more pleased," he added. "Unfortunately we were 2-0 down.
"The first goal is a typical Arsenal goal, sometimes you've got to hold your hands up and say it's a real quality goal.
"But a big turning point in the game we're talking about is a refereeing decision again, which I think everybody in the ground expected to be a free-kick.
"We didn't get it and again a bit of quality from Arsenal, a terrific finish by Podolski and after playing really well we're 2-0 down at half-time.
"Sometimes it is cruel but that's what this big league is all about, they're capable of it because of the quality of the players they've got."
