The Dons went down 1-0 at St Mirren Park to leave them with one point from their first two SPL games.
Celtic beat the Dons five times last season, including a 9-0 win at Parkhead in the SPL.
However, Pittodrie boss Brown insists his players will be inspired rather than cowed by the prospect of a Hoops visit.
"After a bad result such as we had last week the best possible game is a game against one of the Old Firm sides," he said.
"It is a bigger crowd, bigger opponents and the players are more in the spotlight so, with that in mind, the Celtic game will take care of itself.
"The results weren't good against Celtic last season but once or twice the performances were okay and they were mitigating circumstances in two of the league games.
"We lost 1-0 at Celtic Park and had two great chances near the end and at Pittodrie we had a player sent off after two minutes.
"Even in the Scottish Cup semi-final defeat, it was was a while before they got the goal and again we ended up with 10 men.
"Hopefully we will keep the full team on the pitch this time but I'm optimistic and there is no sense of apprehension at all.
"It will be keenly anticipated and the players are all looking forward to it.
"Celtic have a big squad, and plenty of players to choose from but a good result is just around the corner and hopefully it is on Sunday "
The former Scotland boss, however, does not have his selection troubles to seek.
Ryan Jack, who was sent off against St Johnstone, is serving the second of a two-match ban - the new punishment for serious foul play - while Chris Clark (knee), Youl Mawene (hamstring) and Fraser Fyvie (groin) are all doubtful.
Brown said: "We were arguably four short last week from what we consider to be our strongest side.
"Ryan is still suspended and I would think the injured players are all in the 70 per cent category, in terms of their chances of playing
"None are certain starters but we can rule none of them out."
Source: Team Talk
Source: Team Talk