The Hoops midfielder will collect the Scottish Premiership trophy after the last game of the season against Dundee United at Parkhead on Sunday and if Neil Lennon's side avoid defeat then only Aberdeen will have taken all three points from them in 38 matches.
The Dons' 2-1 win over Celtic at Pittodrie in February ended the visitors' 26-game unbeaten run but ultimately made no difference to the Hoops' quest for three in a row.
"It's not spoiled the season," said Brown. "We've won the league by nine or 10 games but it is hurting and it's in the back of our heads.
"It's the one that kind of got away. We could have went through the league without defeat but it's not to be.
"We've won the league and that's the main thing.
"In every single league match we've played in we've done really well, even when we were defeated.
"We were a little bit unlucky to go down to 10 men in that game."
Brown is looking forward to getting his hands on the trophy again but the match against United will not be the final appearance of the season for him.
He will play in Scotland's friendly against Nigeria at Craven Cottage on May 28 before he goes on holiday and is pleased that he has remained injury-free in this campaign after having an operation on a troublesome hip last season.
He said. "It's been enjoyable. I knew I could do it.
"I needed the operation at the time. Maybe it wasn't the best idea to hold off but I wanted to play in the last-16 (of the Champions League) like everyone in that dressing room.
"This season has been great for me.
"I've managed to train every day and be involved and that's what I'll try to do from now to the end of my career."
United boss Jackie McNamara may well rest some of his players ahead of next week's William Hill Scottish Cup final against St Johnstone at Celtic Park.
Brown said: "They've got a few injuries as well so it's going to be hard for them.
"But it's not about Dundee United. That day is going to be about us and how well we've done in the league and why we deserve the trophy."