Freddy Eastwood put the Shrimpers ahead in the 70th minute at Roots Hall and then set up Anthony Grant's winner in the 90th minute to condemn the Dons to their third defeat in a row.
"They worked very hard. I was proud with how much they put into it," said Brown. "We decided that we would try to compete with Southend as much as we could and I think we did did that very well for an hour.
"I was a little bit disappointed with the second-half display because the first half had everything I wanted.
"Overall there was not a great deal of football played but I thought we went into the second half with the ability to get the ball down and play, but we did not do that.
"Although I'm very disappointed that it's three games where we have come away with nothing, I will look at the DVD and get the positives out of this. I learned a little bit more about the boys."
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