With Celtic all but guaranteed to take top spot and the Champions League space that goes with it, the teams finishing in second and third places this year will qualify for the Europa League, along with the winners of the Scottish Cup.
Aberdeen exited that competition last week but Brown is confident Europe is still a possibility despite the disappointment of Saturday's 0-0 draw.
Brown said: "Everyone in the dressing room is enthusiastic and I'm still optimistic about a good finish to the season. We've got a dozen games left, and after we lost the first game of the season, harshly, to Celtic we went on an unbeaten run of 11 games.
"I think we can do the same again. There's enough in the dressing room to do that, and we can hopefully get more wins than draws this time.
"I was in the dressing room for quite a while, and there's a real determination to finish with a flourish. We can see that we can be the better team in games and we've just got to translate that into victories."
The former Scotland boss refused to comment on the second booking that saw Mark Reynolds sent off, the defender having been penalised for what referee John Beaton deemed a deliberate handball as he charged down Kenny McLean's 73rd-minute shot.
"You know I never make comment about that (referees), and I'm not going to change the habit."