The skipper was among 13 players who had to isolate following Christopher Jullien's positive Covid-19 test after the club's Dubai training camp.
Depleted Celtic - also without manager Neil Lennon - drew both matches in the players' absence and trail Rangers by 21 points with three games in hand.
"We always have the faith," Brown said.
"We've always got that positivity. We know that we can keep winning games and that's what we have to do to put pressure on our rivals.