Bruce, himself a centre-half during his playing days, feels Bramble will improve once he increases his powers of concentration.
"That's what sorts out the top players from the not-so-great players," said Bruce. "The top players don't make many mistakes, and even if they do make one in a season then that's too many for them.
"Of course, everybody makes a mistake, but the top players pride themselves on not doing so. But Titus still has it within himself to be a top player, he's only young.
"He just has to learn, and he will, and he will improve. That's why I am here to try to help him if I can."
After leaving Newcastle in the summer, where he often endured a torrid time, Bramble slowly regained his confidence and form as the season progressed despite the Latics struggling at the wrong end of the Premier League table.
The mistakes, though, thrust him back into the spotlight for all the wrong reasons, meaning he now has to knuckle down and again show "strength of character" if he is to force his way back into the side.
Bruce added: "Although he has trained particularly well, I have to say Emmerson Boyce has come in and done a fantastic job. He has been rock-solid and reliable. Titus is obviously disappointed, like most players are when they are not in the team, but he has to show the same attitude he has over the past couple of weeks and force his way back again.
"He has to show strength of character, which he has done all his career, because he has been on the receiving end of some stick on occasions. Make no mistake, he is a good player, but he has a slight problem with his concentration which has cost us dearly.
"That is when I made the decision to pull him out of the firing line, and that is what I get paid for. When you have a squad of 22 or 23 players there are always going to be 11 or so who don't like you or are upset with you.
"But they will play their part, and I'm sure Titus will play his over the next few weeks."