Ahead of their qualifier at Spartak Moscow, Brown declared: "That is why I came here.
"I wanted to show people what I can do. People in Scotland have seen what I am capable of and now I want to show the rest of Europe and the world what I can do.
"I have dreamt about playing at this level and now it could come true," he said. "I just go into every game like it is my last game and hopefully I can play well. I just have to look at the crowd and then to try and blank everything else out. I want to go across there and to show Celtic can win away from home in Europe.
"It is not really about myself. It is about the whole team and if we do well that is all that matters. There is a lot of expectation on all of us not just me. I hope I can cut it at this level and I hope the team can cut it at this level. We win together and lose together."