The 72-year-old takes charge of his final game before making way for Derek McInnes and the Clydesdale Bank Premier League clash with Dundee United at Tannadice is a must-win match for both teams.
Even then the winners need Kilmarnock to drop points at home to bottom club Dundee to ensure a top-six finish.
Brown said: "Normally it would be a very good fixture, the local derby, but it's now even more important because there could be something at stake.
"If Kenny Shiels' team does its job with a home victory it won't matter really, but it will matter for us from a point of view of pride and eventual league position so it's a good end to the season.
"It's not as good as we would have hoped but it's acceptable. We have to say Kilmarnock are favourites, then Dundee United with home advantage, then ourselves and Hibernian.
"It's a cup final. We've got to try and get a victory. We have to go and challenge them to defend because we're very good when we attack and United will know that."
When asked about the prospect of going out on a high with the help of former club Dundee, Brown said: "It would perhaps be a fairytale, but I think it's not out of the bounds of possibility.
"I thought at one point with the fixtures in front of me, that it was a possibility Kilmarnock could end up with two draws.
"If you were a betting man you would bet on Kilmarnock, but what we have to do is make sure that Aberdeen are the team that will be there if they slip up."