Four days after losing the Johnstone's Paint Trophy final against Crewe at Wembley, United saw their season effectively ended by Keith Hill's resurgent Dale.
Mark Phillips had cancelled out Michael Rose's first-half opener within minutes of the restart but a Bobby Grant brace and an Ashley Grimes finish put the result beyond Southend's reach. Barry Corr, who squandered several chances and hit a post with a header, netted a late consolation.
"We got a lesson on how to play football on a surface that wasn't conducive to playing good football," Brown said.
"Rochdale are renowned for being a good footballing team, but for 90 minutes they did nothing but turn our two centre-halves to face their own goalkeeper. They put balls in behind us and turned us all day.
"Consequently they played in the right areas of the pitch. We didn't. We tried to play in the wrong areas and we got caught out."
Brown continued: "I felt it was harsh to go in one down at the break. We got ourselves back into it but then basic individual errors after that have cost us dearly.
"I have a striker, Barry Corr, who could quite easily have walked away with the match ball, but we still wouldn't have won the game. If you cannot defend properly and you cannot play football in the right areas you are going to get beaten. Margins in football are fine, but if you don't get the basics right you are going to lose games.
"I have defenders who thought they had a good game because they kept possession and played football. It's not about possession, it's about sticking your head in, kicking it as far as you can on a surface like this and getting your strikers to hold the ball up so the midfield can support them. We didn't do that all night."