Brown had to leave on-loan Wigan defender Rob Kiernan and on-loan Fulham forward Cauley Woodrow on the bench after they both got stuck in traffic on the M25.
But Brown felt the alterations actually helped the Shrimpers come out on top in a game which saw three red cards.
"It's amazing what football can throw at you but the late changes probably worked in our favour in the end," said Brown.
"I named the team on Wednesday and we had been working with them for a few days and then, at the very last minute, we have to make changes because of the traffic.
"That gave Michael Timlin a chance in the midfield and I thought he was outstanding.
"His experience in the midfield was important but all the players deserve credit for how they adapted to what happened.
"I also hope we put a smile back on the faces of our fans after what was probably our worst performance of the season against Newport last weekend."
Both teams had players sent off in the first half with on-loan Mansfield striker James Alabi, making his debut after signing from Stoke this week, and Southend midfielder Conor Clifford seeing red.
The Stags finished the game with nine men after midfielder Lee Beevers was dismissed in the closing stages after receiving a second yellow card.
In between the red cards there were also goals. Anthony Straker struck after 25 minutes and a Alan Marriott own goal a minute before half-time sent the Shrimpers into the break in control. Kevan Hurst, once of Chesterfield, completed the scoring in injury time.
Mansfield manager Paul Cox was furious with the display.
"I can only apologise to our fans that have travelled because that just wasn't good enough," said Cox.
"We played poorly but things didn't go our way either.
"I thought the red card on first view looked harsh but I can't make a comment until I have seen the replay.
"I'm still confused by the second goal we conceded because we viewed it at half-time and I've been told he wasn't over the line, but these things happen.
"I can only reiterate how poorly we performed and I said a few words to the boys afterwards but I will keep that between me and the team."
- Sports & Recreation
- Michael Timlin