Neil Lennon's Celtic side have won 17 Clydesdale Bank Premier League games in succession and 20 in all domestic competitions. The seventh-placed Dons are themselves unbeaten in 11 games since December 24, a run which has moved them clear of the SPL relegation zone and into the quarter-finals of the William Hill Scottish Cup.
Brown said: "We have to acknowledge how excellent they have been. Their team has been fairly consistent and they haven't had too many major injuries, unlike ourselves, and I think the results Celtic have achieved has come from consistency of selection. They will not take the foot of the pedal, that is certain, I don't think Neil Lennon would allow that."
He added: "Neil Lennon is an outstanding operator and you underestimate him at your peril. You cannot fault the run he has Celtic on right now."
Nevertheless the Dons are in optimistic mood as they seek to move into the top half of the SPL with the split approaching. Brown's side are currently four points behind sixth-placed Hearts.
Brown added: "Every week we are confident. Since the beginning of the season there has always been a good atmosphere and an upbeat disposition at the club and it is no different because we are playing the best team in the country, in fact that is an added incentive."
The Dons are eager to test Celtic.
"We never go out to defend the game and we never go out looking for the draw," Brown added.
"We play appropriately but I don't think any team I have sent out has been sent out with a defensive mentality. They have three of the top strikers in the SPL in (Gary) Hooper, (Georgios) Samaras and (Anthony) Stokes and St Johnstone have the other two.
"We managed to curtail the St Johnstone two and if we do the same against Celtic I will be pleased - but we need to get one at the other end to take the pressure off the defence."