Franco Smith's side sit top of the league but two of the remaining three games are away in South Africa, against Bulls and Lions.
A top two finish would guarantee a home quarter-final in the play-offs, and indeed a home semi-final if they get there, and Brown has challenged Warriors to capitalise on their good work so far this season.
"[A top-two finish] has to be the target," Brown told the BBC Scotland Rugby Podcast.
"At the start of the season, or even pre-Six Nations, you're talking about top four, because you want that home quarter-final. It's so hard to win away from home in the play-offs.
"The big looming shadow being that if you don't get a home quarter-final or semi, you're probably going to be away to a South African team.
"The prospect of getting top two and having a home quarter and semi is something that you have to grab with both hands.
"It's going to be a big challenge over the next three weekends, but I've got full confidence we can go there and do it."