Brown's Shrimpers side were worthy 4-1 winners over Championship outfit Millwall on Saturday, following up previous impressive wins at both Morecambe and Chesterfield.
And their reward is a fourth-round tie at home to Premier League Hull, whom Brown managed between 2006-2010 - leading the club to the top flight for the first time in their history.
Brown told the club's official website: "You couldn't write the script, it really is what the FA Cup is all about.
"I am looking forward to the game, but I won't be thinking about it at all until the week before, after we've played Plymouth and Chesterfield in the league.
"It's a great draw for me personally coming up against Hull, but also for the players to test themselves against a Premier League side.
"We've beaten two teams from our division, two good teams, and then convincingly beaten a Championship side, so we deserve a crack at Hull."
Brown has been in charge of Southend since March last year and has already started to stamp his mark at Roots Hall.
As well as reaching the fourth round of the FA Cup, the Essex outfit currently sit fourth in League Two and have their sights set a first return to the third tier since 2010.
Brown added: "One of my ambitions when I arrived at Southend was to fill the stadium and I think we can do that against Hull.
"Especially with the performance against Millwall and hopefully two good performances against Plymouth and Chesterfield.
"I know Steve Bruce (Hull boss) very well, we get on, and he's got a good team together, so it'll be a cracking FA Cup tie.
"It's also nice to have the draw at home. If we're going to try and go further in this competition, I felt it was important we were at home.
"As I say, there's two big games before then which the players need to focus on, but it's a game we can all look forward to in the near future."