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.
Having exceeded expectations in Europe by beating Barcelona en route to the last 16 of the Champions League, there is little room for improvement other than adding the Scottish Communities League Cup to their haul while repeating such impressive form on the continent.
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."