Brown played in Edinburgh's only European semi-final in 2012 and has been in stellar form this season - starting 12 games and crossing once.
One-cap Scotland winger Brown said Edinburgh's focus has been on regaining their place in the top European competition and after finishing eighth in last year's GUINNESS PRO12, they now sit in seventh and Brown insists they are heading in the right direction.
"We set goals at the start of the season and that was definitely one of the main ones, so there is a massive focus on making sure we do that and get back into the top tier," he said.
"There is a real good atmosphere here at the moment and a sense of expectation about the next couple of years ahead.
"We've shown in parts this season what we can do and we just need to get the consistency up there.
"There's been a couple of results we've been disappointed with but I think we have real potential as a club.
"This World Cup season has tested our strength in depth but it's been positive having the young lads coming up and getting some game time. That will put us in good stead for the next couple of seasons."
Edinburgh have not lost at home - other than to an Irish province - since April 2014 and they will be hopeful of claiming a result against the Italians, who were beaten comfortably 47-0 by Munster at Thomond Park last time out.
Zebre triumphed 19-11 at the Stadio Sergio Lanfranchi and Brown is relishing the prospect of rectifying the mistakes they made in Parma and taking on Glasgow Warriors-bound Italy wing Leonardo Sarto.
He said: "Last time we played them was the week they got their international boys back from the World Cup and it obviously boosted them.
"They can play and throw the ball around so we have to be wary but we will focus on our game. It's a big opportunity for us.
"Leonardo is a good, rangy player. I was up against him earlier in the season when he'd just come back from the World Cup.
"He's tough to put down but we'll all have to win our individual battles and they have good players through their team. We'll have to shut them down."
Guinness PRO12 Edinburgh News
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