The Glasgow giants picked up the first silverware of the season by downing Aberdeen at Hampden Park to claim the Scottish League Cup.
Celtic are the current pacesetters in the Premiership, with an eight-point lead over their nearest rivals and they travel to Albion Rovers in the fourth round of the Scottish Cup in January.
The Parkhead club are well placed to battle for further domestic success this term but Brown insists they still have plenty of work ahead.
The midfielder also paid tribute to boss Brendan Rodgers and dedicated the League Cup success to the Northern Irishman.
“I think it was important for us that people can see that we are giving something back to him [Rodgers] in terms of our performances,” Brown told the Evening Times. “He has come in and got the place buzzing and he has us as a team playing really good football so it was nice for us to give him a trophy.
“Everyone talks about a Treble but we have won one and we’ll just see where it goes from there.
“I think it is huge for the gaffer. Everyone can see the direction that we are going in. It is a wee marker from us.”