Blues' defensive qualities formed the foundation of them finishing ninth in the Premier League last season.
But during the current campaign they have pressed the self-destruct button with a series of unforced errors.
But there were encouraging signs in Saturday's goalless draw at Manchester City even though Birmingham dropped into the bottom three.
Carr said: "We have enough in that dressing room to be safe. But if we keep conceding silly goals, we won't be safe.
"There have been penalties, own goals. If you look back, they have been poor. A lot of the goals have been gifts.
"If we just cut that out, we are quite solid in general as a team. We know the target we have to get to be safe. It's going to be tough again.
"It was good to get a clean sheet and a draw away from home against one of the big sides. It was a good confidence boost to the lads."
Carr believes the relegation picture will not become clearer until the New Year.
He said: "It won't be until after Christmas, even until a bit later, that you are going to see the teams that are really going to be in the mix.
"It's going to be tough and there no are teams you could definitely say look as if they are going to go down.
"I think it is going to go right to the end and there will be a few good teams in there."
Carr added: "A few teams can say they are one win away from mid-table but it's about getting those wins. They are hard to come by in the Premier League now.
"Games are so tight but the good thing is it has been shown that everybody can beat everybody. It's a strange league this year."