General synonyms:
* Distractedly
* Thoughtlessly
* Unconsciously
* Mechanically
* Automatically
* Inattentively
* Mindlessly
* Without paying attention
Synonyms that emphasize a lack of focus:
* Dreamily
* Vacantly
* In a daze
* Lost in thought
Synonyms that emphasize a lack of intention:
* Unintentionally
* Without thinking
* Spontaneously
Synonyms that emphasize a sense of detachment:
* Remotely
* Detachedly
* Distantly
The best synonym to use will depend on the specific meaning you want to convey.