The Parkhead outfit’s cross-city rivals, under new manager Steven Gerrard, had enjoyed an unbeaten start to the new season both at home and abroad ahead of the Old Firm derby.
Oliver Ntcham’s second-half score however was enough to ensure that Brendan Rodgers’ side came away with the three points and local bragging rights as they extended their unbeaten streak in the fixture to 12 games.
Brown, the former captain of the Scotland national team, has featured in his fair share of Old Firm fixtures since arriving at Celtic Park in 2007 and acknowledged that he was pleased with the result.
“Performance wise it was exceptional. From start to finish, we dictated,” the 33-year-old said.
“They came to Celtic Park and we pretty much showed them who was boss for 90 minutes.
“The lads have been outstanding these last two seasons and it’s about kicking on now. They didn’t want to press us too high up the park because they had a hard game in midweek and they were probably a bit leggy.
“We’ve got a great team spirit and we showed it again on the park. We celebrated together. But when we lose we also lose together and that’s what a good team does.
“Craig [Gordon] has had one save to make in 90 minutes. If it hadn’t been for Allan McGregor then it could have been a bit more.”
For the first time since former Liverpool manager Rodgers arrived in Glasgow two years ago, Celtic have endured a rough month or so, following a failure to qualify for the Champions League group stages amid a fraught transfer window, though Brown maintains that the squad have not lost their focus.
“People can question us all they want, but it’s about team spirit and what we do in the dressing room,” he added.
“There’s always going to be hard days but it’s about how you come back.
“We don’t read too much in the press or in social media. We just stick together and work as hard as we can.”