The Scots were drawn alongside Germany, Poland, Republic of Ireland, Georgia and Gibraltar in Group D for Euro2016 qualifying, which kicks off in September this year, and midfielder Brown is targeting a successful campaign.
Scotland have not competed in a major tournament since the 1998 World Cup in France but Brown is hoping that changes for the UEFA tournament in the same country in just over two years.
"To reach the finals would be the biggest thing for me. When you're young you dream of playing at the Euros or World Cup," he told the Daily Record.
"I remember France 98 quite clearly and what we did there. There was a great atmosphere with all the Scotland fans over there, and even just watching it on telly it was a huge event.
"We think we're good enough to get there and we just have to prove it now.
"Most of the guys are based in England and playing in one of the best leagues in the world. So if they can do it down there there's no reason why we can't do it at the Euros."
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