The Hoops' Glasgow rivals will not be competing in the top flight after they lost a vote following their spiral into liquidation but Brown is of the belief that it will be a competitive competition even though his sides main title rivals are gone.
"It will be a little bit different, but at the end of the day we still have to go out there and play every game," he told Celtic's official website.
"It's always hard playing at home and even harder going away to teams like Aberdeen and Hearts. We have to make sure we keep our form week in, week out.
"St Johnstone have pretty much the same squad just now as they did last season so I think they will be another strong force."