Bruce, who on Thursday was hit with a misconduct charge by the Football Association, was dismissed as manager of the Black Cats in November 2011 despite overseeing a relatively stable two-and-a-half-year spell at the club.
The 52-year-old got the best out of Darren Bent, who scored 24 league goals in Bruce's first season, and the club finished 13th and 10th in the table before he was replaced by Martin O'Neill.
A mid-table finish seems a long way off for the club now given their poor start, which has put them in real danger of relegation.
But when asked whether Saturday's game at the KC Stadium took on any more significance because of his history with Sunderland, Bruce said: "No. No. Not any more. It would be nice to win though."
Hull will fancy their chances of achieving that goal this weekend given their efforts over the last week.
The Tigers lost twice at Spurs in the space of four days, but the hosts had to rely on a controversial spot-kick, and a penalty shoot-out to defeat Bruce's side.
On Wednesday night Hull had looked set for victory in the Capital One Cup at White Hart Lane when Paul McShane scored in extra-time, but Harry Kane's equaliser made it 2-2 after 120 minutes and Ahmed Elmohamady's missed spot-kick sent the visitors crashing out.
Bruce's squad remains ravaged by injury, but he thinks his players will be desperate to bounce back from an energy-sapping encounter at White Hart Lane.
"It will be a long ride home and then we have to get ourselves ready for the weekend, but knowing the players the way I do, they'll be motivated and ready for Saturday," said Bruce, who made four changes for the fourth-round match.
"We don't have the luxury of being able to make (eight) changes like Tottenham did. We don't have the resources, but they will give me everything they have got.
"If they are fatigued, they are fatigued, There is nothing I can do about that. But they will give it their best shot."
Jake Livermore and Tom Huddlestone will return after sitting out the cup game while Robert Koren and Danny Graham both returned after their respective spells on the sidelines.
Still, Bruce had to leave out five first-team players due to injury and now his son Alex Bruce is a doubt for the Sunderland game after hobbling off in the first half at White Hart Lane.
"He has a bit of a groin injury," Bruce said of the defender.
"The one thing you can't do is mess about with muscle injuries.
"I don't think he will be ready for the weekend, and we have one or two who have picked up a few knocks, but we will see how we do."
To compound Hull's misery, Bruce's misconduct charge following last weekend's 1-0 defeat at Tottenham has been confirmed by the FA.
Bruce described referee Michael Oliver's decision to award a late penalty in north London on Sunday as "a joke" and the FA confirmed the charge on Thursday morning.
A statement read: "Hull City manager Steve Bruce has been charged for misconduct by the FA in relation to post-match media comments he made following his side's game against Tottenham Hotspur on Sunday 27 October 2013.
"It is alleged Bruce's comments called into question the integrity of the match referee, and/or implied that the match referee was motivated by bias; and/or brought the game into disrepute, in contravention of Rule E3(1).
"Bruce has until 6pm on November 4 to respond to the charge."