Celtic won the title with only three games to go; their three victories over Aberdeen proving pivotal over the season.
And showing commendable dignity, particularly compared to overweight midfielder Kris Commons' disrespectful comments last week, Brown admitted the Dons put his team under pressure until the last.
He said: "It was a good challenge from Aberdeen all the way. It's always hard, especially when they keep pushing. Our games were on Sundays, theirs were always Saturdays.
"But we kept fighting, we kept playing attractive football, and that's what we try to promote at this club.
"You always look at whoever is second and third, especially at the start of the season we were a couple of games behind. We were playing catch-up and we knew we had to win games to put Aberdeen under pressure and we managed to do that."
Brown would like to complete a clean sweep of victories over the Dons, but knows that the Reds will be up for it on Sunday.
He added: "It's always hard going up to Aberdeen. They are a good team, they try to play football and it should be a good game.
"Every game we have played against them they have made it hard. We have struggled at Pittodrie in the past, but this season we did very well, we got a late goal as well. I think that kick-started our season going up there and winning away from home, in the 91st minute as well."
Source: Yahoo/PA Sport