“I’m not really interested in Wembley just yet, we have got to stay in this league and let Wembley look after itself in four weeks or whenever it is,” Bruce told reporters after Sunday’s defeat.
“We have got to concentrate on the next few games and make sure we get over the line because we haven’t done it yet, we are not safe yet and we still have a bit of work to do and that’s all I’m concentrating on.”
Hull face trips to relegation-threatened Fulham and Aston Villa and the manager’s former club Manchester United next before finishing their campaign at home to Champions League chasing Everton on May 11.
Hull have enjoyed a strong campaign but five defeats in their last seven games have left them short of the traditional safety mark of 40 points, although that is expected to be a lot lower this season.
Bruce was also left nervous by the recent improved showing of the teams beneath them in the table with bottom side Sunderland taking four points of title chasing Manchester City and Chelsea in their last two matches.
“I always said if you get 10 wins that is usually enough and it still might be, who knows,” said Bruce, whose side achieved their 10th league win of the season at home to Swansea City earlier this month.
“Its too close for comfort and we have seen some unbelievable results at the weekend and its concertinaed it and its quite a remarkable league this year.”
Despite the defeat to Arsenal, Bruce was pleased with the way his team performed on Sunday.
Strikers Nikica Jelavic and Shane Long, who will both miss the cup final as they played for others clubs in the previous rounds, went close to putting Hull ahead with Jake Livermore also hitting the inside of the post with a long range strike.
But Aaron Ramsey opened the scoring for the visitors in the 31st minute after a swift attack with Lukas Podolski doubling the lead just before halftime and added a third after the break.
Bruce, though, was annoyed Jelavic was not awarded a free kick after a coming together with Mikel Arteta which led to Arsenal regaining possession and scoring the second.
“The big turning point in the game, we are talking about a refereeing decision again,” the former Wigan Athletic, Sunderland and Sheffield United manager said.
“Everybody in the ground expected 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, really well we are 2-0 down at halftime.
“It is cruel but that’s what this big league is all about, I keep saying they are capable of it because of the quality of the players they have got.
“Towards the end it is very, very easy for them, but the first half in particular it’s the best we have played for weeks and I couldn’t have been more pleased.”
(Writing by Patrick Johnston; editing by Amlan Chakraborty)