The Hoops demolished Hearts 4-0 at Tynecastle on Wednesday night to open up a four-point gap over Rangers at the top of the Scottish Premier League.
It was Celtics 13th successive league win -- their best run since 2004 -- and was a measure of revenge for their last defeat in the SPL, a 2-0 loss to Hearts in October.
Brown believes the emphatic victory over Hearts was Celtics best performance of a campaign which has seen them go from 15 points behind Old Firm rivals Rangers to four in front.
However, the midfielder, who scored his fourth in four games in the match against Hearts, is adamant the best is still to come from the Hoops.
"We have always got to keep complacency in the back of our mind as we know our run can easily come to an end," the Celtic captain said.
"But we are confident just now heading into games and we are looking forward to them. We are getting better and better every game. We are getting stronger, fitter and looking good.
"I dont think anyone is unstoppable but we are just taking it one game at a time and seeing where we can go."
The Hoops face Inverness for the second week in a row having knocked Terry Butchers side out the Scottish Cup last weekend.
And while the Inverness manager heaped praise on Celtic he says all the pressure will be on Neil Lennons side at Parkhead.
"Celtic, without doubt, are the best team in Scotland," Butcher said. "Theyve certainly got the best squad in Scotland.
"They are scoring goals and winning games. They are steamrolling everybody.
"We have to make sure were not part of a demolition job. We generally give Celtic a good game. They have to work hard to beat us.
"Weve got nothing to fear. All the pressure will be on them to continue their run. All the pressure will be on them to get three points."
Rangers have the chance to increase the pressure on their rivals before they take to the pitch at Parkhead when they take on Dunfermline in the early kick-off match at East End Park.
These are dark days for Ally McCoists side who were knocked out of the Scottish Cup by Dundee United last weekend.
With the departure of Nikica Jelavic to Everton, and injuries to Steven Naismith and Kyle Lafferty, the Ibrox club have been left short of strikers.
But McCoist is hopeful of re-signing former striker Daniel Cousin, who is a free agent, to bolster his squad.
"It goes without saying its a department we definitely need strengthened in," said McCoist.
"So we are hopeful that we can get things finalised and get him over here. Ive watched his performances in the African Nations Cup as well and he is very keen to come."
Gabon striker Cousin may not arrive in time for the match against Dunfermline but Rangers will still fancy their chances of victory against the side bottom of the SPL and the only team in Scotland yet to win at home this season.
Fixtures (1500 GMT unless otherwise stated)
Saturday
Dunfermline v Rangers (1200), Celtic v Inverness CT, Hibernian v Aberdeen, Kilmarnock v Hearts, St Johnstone v Dundee United, St Mirren v Motherwell
Source: AFP
Source: AFP