Millwall gifted their opponents a sixth-minute lead when keeper David Forde failed to deal with Dan Harding's free-kick and Alex Revell fired home through a crowded area.
Brkovic should have drawn the sides level 10 minutes into the second half, but his shot from six yards lacked power and went wide of a post.
Even the introduction of veteran striker Neil Harris on the hour did not look like galvanising Millwall, and it was Southend who almost added a second three minutes from time when Lee Barnard's long-range shot went wide.
However, it was Millwall who had the final say.
Marc Laird hit the woodwork from the edge of the area, the rebound fell to Harris but Steve Mildenhall saved before Brkovic prodded home the rebound.