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Definition of drowsy : 1. Disposing to sleep; lulling; soporific.
2. Dull; stupid.
3. Inclined to drowse; heavy with sleepiness; lethargic; dozy.

Synonyms:

moderate, drowsing, awareness, nodding, slumberous, lingering, gradual, dozing, yawning, dawdling, slumbery, slack, dozy, procrastinating, deliberate, inattentive, inactive, oscitant, asleep, inert, tardy, somnolent, dilatory, delaying, napping

comatose, soporific, besotted, doltish, dim, slow, cloddish, blunt, sleepy, apathetic, obtuse, dull, loutish, benumbed, thick-witted, stupefied, ponderous, stupid, lethargic, bovine, boorish, sluggish, dense

languid, indolent, lazy

droopy, worn-out, blue, debilitated, wayworn, footsore, listless, faint, trying, feeble, uphill, depressed, frazzled, exhausted, bored, over-weary, limp, tired, toilsome, wasted, run-down, fatigued, weak, cheerless, flaccid, weary

enervated, flagged

Usage examples:

• Couldn't get my nap i' the chair 'safternoon, and it makes a man a bit drowsy." - "The Man with a Shadow", George Manville Fenn.
• While he was in this drowsy state the door opened and Henry appeared. - "Marguerite de Valois", Alexandre Dumas.
• The men were tired and somewhat dejected as they sat about the blaze with their damp blankets round them, but by and by Blake, who had been feeling drowsy, looked up. - "Blake's Burden", Harold Bindloss.