The Celtic midfielder has been buoyed by the side's improvement under Gordon Strachan and hopes to bow out of a fruitless qualification campaign with a win against Croatia
Although Scotland's hopes for qualifying for the World Cup next summer were ended some time ago, they remain in a scrap to avoid finishing bottom of Group A.
Despite their struggles, Brown feels the side are progressing under former Celtic manager Strachan and is confident of beating Croatia, just as they did in Zagreb in June.
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"I think we've learned a lot in the last four or five games. The new manager has come in and told us what formations to play, when to press, when not to press. We have learned a lot under Gordon.
"We've had an enjoyable week of training at high intensity and we're ready for the game. They still have a lot to prove. Hopefully the qualifier [against Croatia earlier this year] is in the back of their mind also."
Brown also praised the impact of Ikechi Anya, who scored in the 2-1 win over Macedonia in just his second Scotland appearance, and believes it highlights the work being done by Strachan to improve Scotland.
Brown added: "Ikechi has been a great player to come in. It shows you the gaffer is working behind the scenes to bring in quality players. What he has got is pace and talent."