"Oh, I feel bad" is a phrase used by people that don't really feel bad, they're just trying to make you think that they are nice and actually feel something for someone else. It's typically used in a very condescending manner as if to say "that poor creature is so pathetic".
Nancy: Hey Julie, who is this tard
sending me a facebook friend request.
Julie: I don't know....oh wait....I think he's the slow kid that use to run around collecting the basketballs in High School. He just sent me a message saying he misses seeing me everyday.
Nancy: Didn't you graduate from High School 20 years ago?
Julie: Yes, creepy....Oh, I feel bad....
Nancy: yeah, right...sure you do Julie.