Goals in each half from Ben Reeves and Jason Banton saw Dons establish a comfortable advantage which was only threatened late on after Roy O'Donovan reduced the arrears.
Dons would have been out of sight had it not been for Cobblers goalkeeper Matt Duke, whose heroics helped Bradford into last year's final.
Boothroyd said: "It was a good cup tie but we showed them too much respect in the first half. In the second half we got on the front foot and asked more questions of them."
Praising Duke, he added: "We had enough chances to get back on level terms but before that we had Matt Duke to thank for keeping us in the game.
"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."
- Sports & Recreation
- Jason Banton