Just to add to what Anil said, use a slicker brush for this purpose. It's very comman that we use traditional bristle brush which is meant to just brush off dust or dead hair on the upper coat. Slicker brush can go right into the inter coat and gather dead fur straighaway. After slicker brushing, you can then use a bristle brush to brush off an fur which slicker brush missed.
I had the same problem about 3 month ago and I owe Anil a lot for helping me manage it in a better way!