The Dons were impressive 4-1 winners over St Mirren at St Mirren Park, showing their clinical side with goals on the counter-attack, Niall McGinn among those on the scoresheet in a fine all-round display.
That was enough to take Aberdeen on to 20 points, level with Hibernian and Celtic, who are both in action on Sunday, but Brown said: "I have always underplayed my hand in any circumstances.
"There's no way anyone other than Celtic will win the SPL, and it's an opinion which I think can be substantiated when you see Celtic, with six first-team players missing, beating Barcelona.
"I hope we will be up competing but to think any club other than Celtic will win it is either naive or optimistic."
Brown believes that 18-year-old Ryan Fraser would be the complete player if he was to follow McGinn's example in front of goal.
He added: "The one deficiency in Ryan's game is scoring goals. He crosses it well, he beats a man but he doesn't score enough goals and McGinn is the opposite, he scores all the time.
"McGinn would even be better if he was bit more big-headed, outgoing and full of himself but he's an introverted type of chap."