Brown lifted his second trophy in two weeks after the Clydesdale Bank Premier League champions beat Hibernian 3-0 in the William Hill Scottish Cup final at Hampden. But Brown is determined to keep the team progressing following their impressive display at Hampden.
"It's huge, not just for me, for every single player and the management staff as well, for everyone at Celtic," he said.
"It's a great club and the support we get week in, week out has been fantastic, so it's something to give back to them. We've got a great squad and hopefully we can keep the players. That's what we are trying to do. We have had a great season this year but we need to try and better it next season.
"We have three qualifiers coming up and we are back in quite early. Hopefully the squad can stay together but that's not up to me."
Manager Neil Lennon's next challenge could be his attempts to persuade Gary Hooper to stay at Celtic Park.
The 25-year-old netted twice against Hibs in what could be his last game for the club. Celtic rejected several offers from Norwich for Hooper in January but the English striker has so far resisted attempts to extend his contract beyond the end of next season and the club may cash in this summer.
With midfielder Victor Wanyama and goalkeeper Fraser Forster also the subject of transfer speculation, to a lesser extent, Lennon will hope his squad remains intact for the first of a potential six Champions League qualifying games in mid-July.
Another player whose future is uncertain is Hooper's Hampden strike partner, Anthony Stokes. The Irishman played a significant part in all three goals, his dangerous crosses with either foot twice setting up Hooper before a great piece of skill and pass allowed Mikael Lustig to cross for Joe Ledley to make it three. The 24-year-old's contract is set to expire but he has been in talks with over a new deal and his Hampden display has reinforced his worth to the club.
"Stokesy works really hard and once he's running at defenders, nobody knows what he's going to do," Brown said. "He's got goals in him and he creates chances as well, he showed what a top-class player he is."