Cobblers fans were taunted after the fixture at Valley Parade after having earlier paid fulsome tribute to the victims of the Bradford fire.
City's statement read: "Club officials were delighted at the gracious response of visiting fans.
"For those supporters then to be abused and threatened is unacceptable.
"Northampton Town fans and fans from other clubs have shown their respect for Bradford City and its supporters. For a significant minority to behave in the way they did is unacceptable."