General opposites:
* Carefully
* Thoughtfully
* Deliberately
* Attentively
* Conscientiously
* Methodically
* With precision
More specific opposites:
* With precision: (if the context is about doing something with accuracy)
* With intention: (if the context is about doing something with purpose)
* With caution: (if the context is about avoiding risk)
* With diligence: (if the context is about putting in effort)
It's important to consider the specific situation and the nuance of "carelessly" to choose the best opposite.