Defeat at Bradford leaves the Cobblers in 11th place in League Two, three points behind 7th placed Dagenham & Redbridge.
A win at home to Bury next weekend would need to be coupled with defeats for Dagenham, Port Vale and Chesterfield to ensure a play-off place.
Gareth Evans did the damage for the home side on Saturday, netting twice against 10-man Northampton, for whom Dean Beckwith saw red in the first half.