First-half goals from Cauley Woodrow and Kevan Hurst did the damage for the Shrimpers, who have now won five of their last seven league games at sit nicely in the League Two play-off zone.
"I am an honest manager and I have got an honest bunch of players," Brown said. "They have responded to any kind of criticism with some fabulous performances of late. We have got three wins and three clean sheets on the bounce.
"If the players keep performing like they are doing then people will find it difficult against us. We performed with that bit of quality in the first half that got us the 2-0 scoreline but second half they did throw the kitchen sink at us but we stood up to it manfully.
"We have fallen upon a system that suits everyone at the club. Barry Corr couldn't make the starting line-up and Cauley got himself a goal. Both goals were from great crosses.
"Players are playing with confidence and it is making sure we keep hold of that confidence because it can be fragile in any division."
Exeter manager Paul Tisdale feels he could be at a point with his squad where changes need to be made.
With no money to spend and his squad under contract, it could present a great opportunity for the youngsters at St James Park.
One of those, 17-year-old second-year scholar Matt Jay was handed his full debut and Tisdale was delighted with his performance.
"We can't make signings, that is not something we are going to do, I need to look at players making strides within the squad," he said.
"I made a decision to play Matt Jay because I think he deserved to play and he was wonderful. I thought he was our best player in the first half. He got his selection off the back of his performances in training and Under-21 games and he did extremely well."
Tisdale added: "We were dreadful in the first half. We were 2-0 down and the players gave it a go, but that's not what we want to be doing every week.
"I think we are at a point now where we have just lost three league games in succession and we need an assessment of how we are playing, how the players are performing individually and maybe it is time I need to have a look at things."
- Sports & Recreation