Bathtub drain leak

The bathtub drain in our upstairs bathroom is leaking. The leak appears to be at the very top where the drain sits into the tub bottom. How can I fix the leak without tearing out the ceiling in the downstairs bathroom?I can get to the plumbing through a opening in the bedroom closet upstairs. But when I feel the drain pipe, I can find a nut to loosen so that I can pull the drain out from the top.As I felt around the pipe coming down from the tub, I found a rubber washer sticking out; it broke into pieces when I touched it. Ran some water in the tub afterwards but no water leaked from the washer.thanks for your help.Mel