The 30-year-old is currently on police bail after being questioned over allegations of sexual assault and possession of a Class A drug.
His club have suspended him as they conduct their own investigation into the matter, but Bruce has expressed his anger over the fact that Bramble was out on the town at all barely 24 hours after his team's 2-1 Barclays Premier League defeat at Norwich.
He said: "There's a police investigation going on into Titus and obviously I'm restricted in what I can say, but for me, the big disappointment is he shouldn't have been there in the first place.
"With the rewards footballers get, they have a responsibility, a moral responsibility, and I don't think footballers should be in nightclubs on a Monday, Tuesday, Wednesday, especially after you have just been beaten - and how badly he had performed against Norwich as well.
"If it was me, I would be locking myself away for 24, 48 hours and burying my head and making sure when training comes around, that I'm going to go and perform better than I did on Monday night.
"That's the disappointing thing for me, but that's what, unfortunately, football has become. With the rewards that they have, they have to show a bit more responsibility."
Bramble is unavailable for the Black Cats' home game against West Brom on Saturday as a result of his suspension.