Having seen off Milton Keynes Dons in the previous round, the Cobblers came from behind to beat Colchester 2-1, with the U's having Clinton Morrison sent-off in stoppage-time.
Henoc Mukendi grabbed the winner after Freddy Sears gave Colchester a first-half lead. Adebayo Akinfenwa equalised shortly after the the restart from the penalty spot before Mukendi had the final say.
"Once the players realised they weren't playing Brazil in their gold shirts they began to believe in themselves," said Boothroyd.
"The team was thrown together a bit because of injuries and maybe we showed Colchester a bit too much respect in the first half. But we played for each other in the second half and got the result we thoroughly deserved.
"It's a cup competition with a trophy at he end of it and we want to do well in it, so I'm very pleased with the result and it sets up nicely for the league game with Exeter on Saturday."