suppose a department manager, he doesn't want to be the kind of person who focuses on details. So he says
I suppose I can be a little bit careless sometimes.
I am afraid that the word careless is not appropriate to use when talking about work, since it usually a bad word.
Cambridge Dictionary gives this definition, which could be a proof.
not taking or showing enough care and attention
Is my understanding right?
Careless means "without care" - saying you deliberately do not take care at work would not reflect on you. Personally, I wouldn't employ somebody who described themselves as "careless".
In the world of business, there are certain recognised management styles, some more authoritarian than others. It sounds like you are trying to describe your management style.
Two recognised management styles are "democratic" - this is a manager who involves their staff in decisions; also "laissez-faire" (a French borrow-phrase) which refers to a casual, relaxed style of management. Some people like this style, others may think it is too casual (careless).
Another term to describe management which focuses too much on details is "micro-management". You could perhaps use this phrase to show the kind of manager you are not. Also, "high-level" management means primarily concerned with major issues rather than smaller details ("low-level")
So perhaps you might say (in context):
I suppose I can be a little laissez-faire at times.
or
I suppose I can be little high-level at times.
