The need to use a dressing on the recently operated eye usually depends on the type of anaesthetic used. If the operation is performed under topical anaesthetic (drops), as is the case for many cataract surgeries, your eye will not need to be covered, although it is a good idea to protect it from any type of bump or pressure using a clear plastic shield.
Following operations requiring anaesthesia of the eyeball, as in the case of retinal or glaucoma surgery etc., it is necessary that the eye is protected and closed with an antibiotic ointment. The eye may remain half-open for a few hours, which could cause major problems if a suitable dressing is not used.