The Hoops take on the Dutch giants in Group H of the Champions League and suspended captain Brown is confident that Neil Lennon's men can record maximum points to follow up from their 2-1 win at home in the last European fixture between the two clubs last month.
"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."
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