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Webster 1913 Edition

adv.

In a drowsy manner.

adv.

Sleepily; heavily; in a dull sleepy manner.

Sluggishly; idly; slothfully; lazily.

drowsily ‎(comparative more drowsily, superlative most drowsily)

In a drowsy manner.
- 1914, Louis Joseph Vance, Nobody, chapter II:
  She wakened in sharp panic, bewildered by the grotesquerie of some half-remembered dream in contrast with the harshness of inclement fact, drowsily realising that since she had fallen asleep it had come on to rain smartly out of a shrouded sky.