The two sides met at City's Pro-Edge Stadium this evening and despite there being 102 places between themselves and the Dons in the English football pyramid, the hosts held out for a 0-0 draw.
With a trip to the Stadium:MK to come, Barrett believes that his City side could spring an upset despite the Dons being odds-on favourites to progress the second time around.
"It's a nice brand new ground and I think they get around 10,000 for league games. Hopefully they won't lose too many of those for a smaller club like ourselves when we come along," he told Sports Mole after the match. "I'm looking forward to that already even though it is in a couple or so weeks.
"I don't think they will have fancied coming here on a cold Friday night, to be honest. Their home comforts might help them out a little bit.
"If we set up the same way and keep it as tight as we can as a team - we know we can do that now. We could rob a scrappy goal, you never know. That's the magic of the FA Cup!"
The keeper made a string saves throughout to 90 minutes tonight, with one in particular from Dons striker Ryan Lowe in the second half receiving high praise.
"It's just one of those things where he has headed it from only five or six yards out. It was just complete reflexes because you don't have any time to think about those type of saves," he said of the stop.
"All those years of coaching have paid of. That was my best save and it was so good to make it at such a crucial time."
Barratt joined City in 2008 having come through the ranks of Luton Town.