Town became the first visiting team to win at St James Park since March, 19 games ago in all competitions, thanks to goals from Jack Sowerby and Mitch Pinnock.
Padraig Amond's leveller shortly after the break was in vain as Cobblers defended resiliently to record a seventh victory in nine league games and stay second in Sky Bet League Two.
Asked if it was a statement win, Brady said: "I don't know about statements but it's nice to break their record because we knew they hadn't lost at home since March and we came here with the aim to end that run.
"To be the first team to win at Exeter since March, I think that shows it was a really strong result for us.
"We found it extremely difficult against the wind in the second-half and we conceded in that 15 minutes after half-time but we got the goal from the set-piece.
"We found a little gap in their set-piece and Mitch ghosts through and gets a great touch on the ball.
"That was important to get back into the lead and to show the resilience and the character we did after that to hold on was brilliant.
"For everyone to work as hard as they did, it's so pleasing as a manager and overall I thought we deserved it."