Rovers are currently in real trouble, occupying the final relegation place ahead of their hugely important trip to Cobblers on Saturday.
But Barton's side were buoyed by a much-needed 2-1 win at home to Doncaster Rovers on Monday afternoon.
And now the boss is in bullish mood ahead of this weekend's crucial clash at the PTS Academy Stadium.
When asked why kind of points total he expects from the final six games of the season, Barton said: "Eighteen out of eighteen, why not?
"We give everyone a game. We gave Sunderland, who are at the top of the league, a game.
"We should win all six games. That’s the intention and that’s the demand."
Bristol Rovers who are two points below Cobblers, face a tough run-in as they take on Lincoln City (sixth in the table), MK Dons (13th), Portsmouth (fourth), Crewe Alexandra (14th) and Blackpool (fifth).
But they are set to be boosted by the return of three key players against Town this weekend, with Alex Rodman, Alfie Kilgour and Josh Grant all potentially available.
"We need all hands on deck," Barton said.
"We hopefully have Alex Rodman back, and we hopefully have Alfie Kilgour and Josh Grant back for Saturday’s game."