Michael Timlin struck the only goal of the game in the second minute of stoppage time to extend the Shrimpers’ winning run to six matches and leave them three points behind third-placed Wycombe with a game in hand.
Southend travel to fourth-placed Bury on Tuesday where a win for either side would thrust them right into top-three contention.
“Exeter are a decent side, I knew it was going to be a footballing test as opposed to a physical test,” Brown said.
“They played more football than us but I think we had more determination than them.
“It is a great game on Tuesday now, everything that you need. It is a six pointer in the true sense of word. It is for the third place. We have won the last five now and six clean sheets on the bounce. I am absolutely delighted with the mentality of the group.
“It is going to be brilliant up there on Tuesday. They are street wise, hard to play against and have one or two match winners.
“Paul (Tisdale, Exeter manager) built it up to be a great game of football before the match, but the ground is still firm and hard and the ball was bouncing up. It was more of a battle than a game of football. We got through it and got the three points which is massively important at this stage of the season.”
Defeat for Exeter means their hopes of making the end-of-season play-offs are virtually over for another season.
“We had to go for it and we played with three centre halves at the end,” Tisdale said.
“It’s very cruel and I find it hard to talk at the moment, although I feel very different to how I did after Wycombe (where Exeter were beaten 2-1 by a penalty 12 minutes into stoppage time).
“It was a different type of game, but it is still very disappointing and very cruel. We are still in it, but we have got ourselves into a very difficult position in terms of making the play-offs now.
“We had chances to stop them from scoring and we could have made different decisions. But it’s happened and I have to say I thought the team played very well, especially in the first half.
“It was disappointing that we didn’t score and that is the danger when you don’t hit the target when we had some really good chances to. That is the story of the afternoon really.
“The players are obviously totally disappointed with the outcome, but you have to ignore those emotions and move on. It’s not over, but it is extremely unlikely.”