The midfielder is ineligible for the UEFA Champions League clash on Wednesday after seeing his appeal against an additional two-match ban for his dismissal against Barcelona rejected.
Brown was forced to watch from the stands during Celtic's 2-1 win over Ajax in the reverse fixture two weeks ago, and believes the club have the qualities to replicate that result at the Amsterdam ArenA.
"The lads are going to have to go there and try to get goals and I have faith they can do it," he told the club's official website. "They showed what a good team they are when they played Ajax at Celtic Park.
"Ajax are renowned for their passing but we still managed to get the ball down. We know they want to play football. It’s great to watch but we can put teams under pressure to make mistakes and it came off really well at home when we pressed them high up the park.
"We've learned how to do that – get the ball back and keep our shape as well. In Europe we’ve been doing really well. We’ve been keeping clean sheets and that’s due to the strikers, midfielders and defenders all working so well together."
Brown will also miss the visit of Milan later this month as he completes his suspension.
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