The 22-year-old was named as the Black Cats' skipper on Thursday but lasted only 43 minutes of Saturday's 2-2 draw with Birmingham.
Cattermole picked up a debatable yellow card early on before going through the back of Lee Bowyer when the whistle had already been blown for offside.
Bruce blasted referee Anthony Taylor for his display but he certainly did not spare his player from blame, and revealed he gave Cattermole the captaincy in an effort to address his disciplinary issues.
"Lee has to learn from it and learn quick because unfortunately, at the moment, he is a target," said Bruce. "His reputation has gone before him and he has to have a little bit more common sense.
"It's too often. I think it's his fourth red card and he's only 22. I love the way he plays the game, his attitude for it, in training, and he's a competitor. But his mistake has cost us.
"I made the decision and I've given it to him to try to give him a bit of responsibility. It was a big call and I certainly got that one wrong (yesterday) but that's what I've given it to him for."
Bruce's frustration was heightened by the fact Sunderland only picked up a point having dominated for much of the game and led 2-0 with only 12 minutes left.
Darren Bent opened the scoring from the penalty spot midway through the first half and the Black Cats' numerical disadvantage initially did not appear to affect them as Stephen Carr headed over his own goalkeeper to put the hosts two up.
But the pressure grew and it was Sebastian Larsson's set-piece delivery that eventually made the difference as he picked out first Scott Dann and then Liam Ridgewell for the equaliser two minutes from time.
Bruce gave full debuts to four players in goalkeeper Simon Mignolet, defenders Nedum Onuoha and Titus Bramble and midfielder Ahmed El Mohamady, while Cristian Riveros and Danny Welbeck came off the bench in the second half.
The Sunderland boss was particularly pleased with his defensive new boys, who also included John Mensah, back at the Stadium of Light for a second season on loan from Lyon.
Bruce said: "I thought Onuoha was terrific. I thought big Titus was terrific and he can only improve because he's done well to play. He had a stress fracture so he's only trained really for the best part of two or three weeks after being out for 12.
"The Egyptian boy (El Mohamady) did very well. I was very, very pleased and if it was 11 versus 11 I think we would have comfortably got the win."
Birmingham boss Alex McLeish began with new signing Ben Foster in goal but did not introduce 6ft 8in striker Nikola Zigic until the second half, and the Serbian immediately proved he will be a handful for Premier League defences.
Zigic's performance was a rare bright spot in what was a poor showing from the visitors, and McLeish expects the former Valencia forward to offer even more once he fully adapts to English football.
The Scot said: "He was a presence and he will cause problems but I'll be expecting a lot more from not only Zigic but everybody. He's got an international pedigree but it's a new league for him.
"Playing in England is completely different to La Liga. He would be starved of balls in La Liga and he would only really get the delivery when he got to the byline.
"The longer ball from the back in English football is something a little bit new for him and I'm going to have to do a wee bit of work on the training ground to help him improve in that respect."