West Coast's two wins – a 33-point triumph over the Western Bulldogs on Sunday and a 50-point win over Port Adelaide in round two – were split by a 97-point thrashing away from home at the hands of St Kilda.
Brown said losses like that might give sides the impression that the Eagles were easy-beats, but wins like Sunday's would quickly prove them wrong.
"We definitely want to make Subiaco Oval our fortress," Brown said at recovery on Monday.
"We've got to show teams that they can't just come over here and think it's going to be a bye week. I think some of the teams might think that.
"We've got to stick up for ourselves and show them it's going to be tough at Subiaco Oval."
Brown said winning away from home and stringing wins together was the next challenge for the Eagles group as it fights to earn back the respect lost in its 2008 campaign.
"Especially with our performance last year, we lost a little bit of that," Brown admitted.
"In 2007, we earned respect winning our first eight games – we've got to earn that back. Certainly winning and winning big games like that yesterday is the way to do it.
"But we've obviously got to get the away wins up and get that consistency together."
With Daniel Kerr receiving a weekly buffeting form opposition taggers this season, Brown said a big part of the side earning back respect was sticking up for the star midfielder.
He said the players didn't look out for each other against the Saints.
"That's not us at all; we don't do that. We stick up for each other and we put our bodies on the line," Brown said.
"It's a team game, so we've got to help each other out, especially the boys like Matt Priddis and Daniel Kerr who are going to get tagged every week. We've got to stick up for those blokes."
Brown praised coach John Worsfold and skipper Darren Glass for their leadership following the round three loss.
He added guidance from Glass and young defender Eric Mackenzie had been crucial in his successful move into the backline following a knee reconstruction.
The young defenders will face their biggest test of the season this week when they travel to Aurora Stadium to take on Hawthorn duo Lance Franklin and Jarryd Roughead on Saturday.
Brown said he would meet any challenge thrown at him by Worsfold, and backed Mackenzie to take on one of the Hawks' forward stars.
"Eric is in great form at the moment," he said.
"He's good enough to match up on anyone in the AFL, I think.
"We're going to go out there and give it everything on ANZAC Day."
