Substitute Danny Crow stole all three points with his injury time strike which cut the gap on leaders Wrexham to seven points.
Speaking to the press afterwards, Brabin said: “I thought it was probably a good game for the neutral.
“I thought we had some really good chances, one in the first half where Alex Lawless is clean through, and you fancy Alex to score them.
“I said at half time, we’re doing it in patches and we just need to be a little bit stronger and a little bit more forceful, and I thought we did that.
Setchell feels Bedford Town deserved their opening point at Stratford
Clubs all set for big kick-off as Bedford Town, Ampthill Town and Real Bedford begin campaigns
Bedford high jumper Gracie takes silver in Belfast
Al Boum Photo joins an illustrious list of back-to-back Gold Cup winners
Hatters desperate to right last season's wrongs against Blues
“We made a couple of subs which penned them back. I always thought we were going to score and we did. To score when we did was fantastic.”
Frustrated County boss Justin Edinburgh added: “We were in a position to certainly get a point out of the game and we haven’t been able to do that.
“It’s crucial times in the game where you’ve got to see the game out
“Good teams punish you and we’ve been punished. We had a chance to punish them (and) we didn’t do it.
“I can stand here and make excuses. The players have got to take a bit of responsibility.”
For all the latest Luton Town FC news, reports, stats, player profiles, live match updates, prediction table and a complete fixture list, visit our Hatters Microsite.