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  Jack Duggan's late winner secured a 1-0 victory on Tuesday and set up a third-round tie at Wycombe in January.
  Stourbridge had gone out in round two in three of the previous five seasons.
  "This has got to be the biggest (achievement) beating a League One side at home," Hackett told BBC WM 95.6.
  "This is what the FA Cup is about."
  Hackett, who has been in charge of his home-town club since 2004, continued: "I thought we were outstanding. We certainly didn't get lucky, we were the better team.
  "It's one of those special nights and it's a great occasion for everybody connected with the football club.
  "Everybody connected with this football club are heroes. I spoke to a gentleman who comes on the coach every week and never misses a game home or away - I told him 'these nights are for you'.
  "Hugh (Clark, Stourbridge president) has been here 50 years and experienced some tough times at this football club, so he gets rewarded. We all do."
  Northampton, who are 13th in League One, started the match four divisions and 89 league places above Stourbridge - who began the day eighth in the Northern Premier League - in the English football pyramid.
  Manager Rob Page told BBC Radio Northampton: "The better team won and that hurts me to say that, but credit's got to go to them.
  "It's a hard one to take and I'm embarrassed at the minute. We'll take any criticism we get and we deserve every bit we get for this."
  The former Wales international defender added: "I apologise for that performance, I didn't expect that at all. Stourbridge deserved their victory, we congratulate them and wish them all the best, but we're all hurting."
target: Manager Gary Hackett said Stourbridge were "outstanding" in their shock FA Cup second-round defeat of League One Northampton as the seventh-tier side reached round three for the first time.