The Dons currently sit in eighth position in the table but are just five points behind second-placed Inverness.
And Brown sees no reason why his side cannot bridge the gap if they can put together a decent run starting with Friday's home clash with Dundee.
He said: "We want success and to finish as high in the SPL as possible. Second place is a target. I am optimistic, always.
"Second place is five points ahead of us so we need a couple of wins to get in touch and I think we've got the capability within the squad to get the wins."
Aberdeen have failed to pick up a single win in 2013 but Brown insists it is too early to judge the success of their campaign.
He said: "I'll look at the table at the end of the season, that is when the table counts.
"You look at the fixtures and think there are points to be gained. I think every manager will be saying the same its just who gets the points.
"Well see at the end where we finish."
According to Brown, the Pittodrie outfit simply need Lady Luck on their side in their coming games.
He added: "We need a break.
"We've missed two penalty kicks this year, which are critical, but I am not too displeased with the way we are playing, in particular the way we are defending.
"No-one is finding it easy to score against Aberdeen.
"We just need to score and I think there will be a transformation in our fortunes."
Dundee travel to the Granite City 15 points adrift at the bottom of the SPL but Brown is taking nothing for granted.
He said: "Every game with Dundee is a close game.
"Just because they are at the bottom and detached a bit, I dont think for one minute that it will be an easy game.
"In fact, it makes them more dangerous."
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