Bruce was sacked as manager of the Wearsiders in November 2011 despite guiding the club to 13th and 10th place finishes in the Premier League.
Martin O'Neill and Paolo Di Canio have since come and gone at the Stadium of Light but Bruce is focused purely on securing another three points as his side look to build on their positive start to the season.
When asked if Saturday's game at the KC Stadium held any more significance due to the way he departed Sunderland, Bruce said: "No. No. Not anymore. It would be nice to win though."
Hull will need to pick themselves up from back-to-back losses to Tottenham in the Premier League and Capital One Cup, although Bruce's players can take heart from the manner of their defeats.
Spurs had to rely on a spot-kick to win Saturday's league clash at White Hart Lane, and a penalty shoot-out to see off Hull on Wednesday night after the game had ended 2-2 after extra-time.
Jake Livermore and Tom Huddlestone will return against Sunderland after missing the cup game, while Robert Koren and Danny Graham both featured at Spurs after respective spells on the sidelines.
Bruce was still forced to omit five first-team players due to injury though and his son Alex Bruce is now a doubt for the Sunderland game after he was forced off in the first half at White Hart Lane.
"He has a bit of a groin injury. The one thing you can't do is mess about with muscle injuries," Bruce added when asked about the defender.
"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."