The Hoops secured the title for a second consecutive season on Sunday afternoon, as they beat Inverness Caledonian Thistle 4-1.
Brown, who watched the game from the stands, 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."
No side other than Celtic or Rangers have ever won the SPL, which was formed in 1998.