What does the narrator feel about the raven's previous owner?

The speaker does not really know that the raven is a tame bird that has somehow escaped and is seeking shelter with another human. He is only speculating in the following pertinent stanza:

Startled at the stillness broken by reply so aptly spoken,
“Doubtless,” said I, “what it utters is its only stock and store,
Caught from some unhappy master whom unmerciful Disaster
Followed fast and followed faster till his songs one burden bore—
Till the dirges of his Hope that melancholy burden bore,
Of ‘Never—nevermore’.”

The speaker guesses that the raven's previous master was dogged by misfortune, not unlike Edgar Allan Poe himself, and that he must have kept saying or singing something which included the word "Nevermore," until the bird began repeating it. This often happens with parrots, Mynah birds, parakeets, and other birds capable of imitating human speech. They will surprise their owners by uttering a word or phrase without the owners realizing that this word or phrase was so commonly used in the household, or that the bird would be find it appealing out of all the other words it heard. It may be that some words are picked up by birds because they are easier for them to imitate than others. But in any case, the speaker is correct in thinking that birds do not really understand what they are repeating and that this raven is only saying "Nevermore" because it was living with a very unhappy man like the speaker.

Poe himself was an unhappy man because of numerous misfortunes. He was always dogged by financial problems. He was disowned and disinherited by his wealthy foster father. His wife Virginia, whom he married when she was only thirteen, was in extremely ill health at the time he wrote "The Raven," and she died about two years after it was published. He died of alcoholism at the age of forty. Many of Poe's poems and stories reflect his own feelings of melancholy and despair. No doubt the many references to "Lenore" in "The Raven" are to Poe's wife, whom he expected to die of tuberculosis and leave him all alone. 

So the speaker evidently feels empathy for the bird's hypothetical previous owner, assuming he must have been a lonely, melancholy man like himself. In the opening stanzas and elsewhere, the speaker presents glimpses of his own existence:

Once upon a midnight dreary, while I pondered, weak and weary,
Over many a quaint and curious volume of forgotten lore,

Eagerly I wished the morrow;—vainly I had sought to borrow
From my books surcease of sorrow—sorrow for the lost Lenore

The speaker identifies with the man he imagines having been the bird's previous master and assumes that man was hopelessly depressed. The former owner must have had a naturally melancholy temperament to have wanted such a black, croaking, "ominous bird of yore" for a pet. The ebony bird capable of uttering only one word is, of course, a symbol of hopeless depression.