Following the 6-1 Champions League defeat by Barcelona in the Nou Camp last week which ended their European aspirations for the season, the Hoops responded with a 1-0 win over Hibernian at Celtic Park which extended their blemish-free run in the Scottish Premiership this season to 15 games.
Asked if Celtic could remain undefeated through the entire campaign, the Fifer did not rule it out.
"We are a tight group and we are strong, and I think if we put our minds to it we can definitely do it," he told the official Celtic website.
Celtic will have to contend with a heavy festive fixture list which sees them host Hearts on Saturday, before taking on St Johnstone, Inverness and Partick Thistle in the space of six days.
However, the Scotland midfielder said: "It was a hard game in Barcelona and they have done that to a lot of teams - they have done that to Real Madrid as well - but we are back in our normal league position and going about the job the way we should be.
"A lot of teams have been spending 50-60 million pounds to get to the last-16 and our budget isn't as big as that. We managed to do it last year (get to last last 16) and it shows what a good team we have here.
"We have a run of games coming up, especially over the festive period which will be hard.
"The gaffer will make a few subs here and there, change it up and freshen faces, but the lads enjoy playing week in, week out and two or three games a week."
Brown would welcome any fresh additions to the squad when the transfer window opens.
"I don't know who we will bring in," he said. "We will need to leave that up to the manager, staff and board, but whoever comes in will be more than welcome."
Watch Celtic v Hearts on Saturday on Sky Sports HD2 from 12.15pm.