Brown, who watched from the Sky Sports studio as Celtic clinched the title with a 4-1 win over Inverness, pointed to their European exertions - where they reached the last 16 of the Champions League - as evidence.
He said: "It's still been hard for us, we've had the Champions League during the week and then on to playing weekend games is hard.
"We've been lucky enough Rangers weren't in the league but the main thing is we have won this league and it's been a great season.
"Hopefully we can stick together a long time. The lads are doing themselves proud week in week out. To bring something home for the fans, it means a lot for us.
"It's always nervy going towards the end and just getting over the line, but the main thing is we've managed to do it and we've brought the cup home."
Stand-in skipper Joe Ledley said: "At Celtic, wherever you go, league or Champions League, you are always under pressure to win.
"That's what you want as a footballer - to win things.
"It's fantastic to come here and have that pressure and I think we've dealt with it fantastically well this season especially in the Champions League. Hopefully we can just continue that until the end of the season."
Gary Hooper, Celtic's top scorer this season, is aware they will need to re-focus for their William Hill Scottish Cup final against Hibs on May 26.
"The main thing is celebrating this first and then turn to the cup final, win that and do the double," he said.
"We've got a great squad, we've played really well and it showed in the Champions League and it showed today that we're really good at home and we can beat anyone."