The Shrimpers were paired with their Championship neighbours in Sunday's draw having seen off Chesterfield at the Proact Stadium in the second round.
Southend have shown signs of progress this season and are currently riding high in third place in League Two, just one point off the summit of the table. And Brown wants to see just how much they have improved when Millwall visit Roots Hall early in the new year.
"I think it is a brilliant draw in many ways. It's a home tie which is great and always puts you in with a chance," Brown told the club's official website.
"Then it's a local derby if you like and there should be quite a big local interest in the game.
"For me it's a test of how far we've come as a new group in seven or so months.
"They are in the Championship and are a good side, so it'll be a real test to measure the squad and what we've done so far.
"We'll be looking to put in a good performance to show what we're all about on the day."