Fulham looked set to climb out of the relegation zone when they burst into a 2-0 lead just before the hour-mark at Craven Cottage, but Hull produced a stirring fightback.
Goals from Ashkan Dejagah and Fernando Amorebieta put the London club in command, only for Nikica Jelavic and Shane Long to stun the home side with strikes in the last 15 minutes.
The strike duo, who were both signed in January, ensured the FA Cup finalists remain six points ahead of third-bottom Fulham with three games remaining.
And Bruce believes his side should have done enough to ensure they will avoid an immediate return to the Championship.
"If we hadn’t got it (a draw) today we may have still been in it (the relegation scrap)," Bruce suggested.
"Thirty seven points might be enough, it usually is. We have three games to go and they (the players) got themselves into this position. All credit to them.
"We have had a remarkable year. We have been in and around 10th, 11th, 12th (in the table) since September, got to a cup final and hopefully safe with three games to go.
"It’s a remarkable achievement and how fitting that was today and they showed what they are about again."
Bruce believes the turning point in the match came after Jelavic had pulled a goal back, when Steve Harper denied Dejagah a second goal with an important save, and he is adamant that a draw was the least Hull deserved.
He added: "We had a crazy 12 minutes and to be fair you have to say well done to Dejagah, who has cut in and bent one in the top corner and then they have a great header by Amorebieta.
"All of a sudden, from being complete control in the first half we are 2-0 down and thinking, 'where has that come from?'
"To be fair to the manager of Fulham (Felix Magath), he has made a big change (replacing the injured Steve Sidwell with Darren Bent) and in the end they had four up the top end of the pitch and they caused a few problems.
"The turning point was Harper's save at 2-1. At a certain point you think it’s not going to be your day.
"We have hit the post and the bar - twice - but typical of them (the Hull players), the reason we are 13th and in a cup final is you've just witnessed again.
"They kept going and for me rightly got the rewards."
