Goals from Reeves and Banton were enough for the League One side to reach the second round of the Capital One Cup.
Roy O'Donovan replied late on for Town in front of 3,486, a first goal of the season for Aidy Boothroyd's men but the boss was unhappy with what he witnesses in the opening 45 minutes.
"We didn't defend set-pieces well enough and that's something we are usually very good at.
"The players need to show more commitment to defend shots on goal and that's a minimum requirement."
League newcomers Newport County now come to Sixfields on Saturday as Boothroyd aims to get last season's play-off finalists up and running in the league for 2013/14.