The midfielder had an appeal against his three-match ban for kicking out at Barcelona playmaker Neymar rejected and still has two games to serve.
He is unable to return until the final group game in Spain against the Catalans and will watch this week's match and the home meeting with AC Milan from the stand.
Brown, though, will travel with the Celtic party to Amsterdam and said: "I'll
definitely be there and doing my bit off the pitch. But I have every belief that as a team we can go there and get a good result.
"Of course it is disappointing not to be playing, but it's done now and there is nothing I can do about it.
"But look at how Charlie Mulgrew and Beram Kayal played against Ajax in Glasgow when they paired up together in the middle of the park.
"They are more than capable of coping with Ajax over there. I've already told them that."
Celtic will also have Georgios Samaras and Kris Commons back for what is arguably now the most pivotal game in Group H for the Parkhead side.
Avoiding defeat would maintain their ambitions of playing European football of some sort beyond Christmas and the return of two key players is massive for Neil Lennon.
Brown said: "Big Sami has been outstanding for us, not just in the Champions League but in general.
"He really does give us something extra. He has been so consistent at this level and you always feel he has a goal in him as well in these games.
"Having him back will give everyone a big lift. We know that it is going to be a tough ask to go and get a result, but from what we saw when we played them here in Glasgow, I honestly think we are capable of it.
"Kris coming back is another bit of good news. You do need to have a bit of experience and these are two guys who have been over the course and know what it takes to get a result on the road.
"We have a lot of confidence about us. We have matured as a European team, I think, especially when we are playing away from home."
And Brown is hopeful that Samaras will opt to commit his future to Celtic in the next few weeks.
"I'd love to see him stay here," he said. "He has become a really important player and he is a good guy off the field.
"It would be great to see him tie himself to the club. It is good for the club to try and keep the core of the squad together. It is a good unit that we have here and the togetherness is good. Keeping that going benefits everyone."