The Bluebirds secured their safety last month and can only finish either 21st or 22nd in Sky Bet League Two.
But players are fighting for their future and Brown himself is keen to agree a longer term deal at the club after replacing Mark Cooper on a temporary basis in March.
“There’s 700 Northampton fans in town and the reason is to see their team get promoted,” Brown told the North West Evening Mail.
“I’m not saying we’re going to do everything we possibly can to stop that from happening, but I’m going to come up with a game plan that’s going to cause problems for the opposition.
“They’re a top three team, we’re a bottom four team. By definition that suggests they’ve got better quality than us. We have to have our defensive heads on display, our horrible heads if necessary, to stop that from happening.
“If we can prevent their quality from flowing, it’s the next part I’m interested in for next season if I’m going to be Barrow manager.
“It’s when we’ve got the ball, I want to see better emphasis on the quality of the play that we have.
“If we can provide that better quality, and I witness that, there’s a chance players that have been at the club all season might still be here next year.”
Brown has also hinted he will give one or two fringe players an opportunity to impress.
He added: “The most important part is you’re always on show, always on trial in football. That goes for every game you play.
“There’s been players who’ve been on the periphery while they’ve been at the club in the last eight games, there’s been players I’ve only seen in training – there might be one or two of them playing on Saturday.
“If they are, and thinking about their careers, where they’re going down the line, they need to remember that every game is an opportunity.”