The Norwegian has endured a shaky start to his career at Celtic Park, leading to doubts over whether he is the right man for the job.
However, ahead of the team's Europa League opener against Red Bull Salzburg, Brown is confident that Deila will be able to guide Celtic to success in the future.
"You have to have faith in him. Everyone sees the good football we are trying to play. It's all going to come together as soon as possible and hopefully that will be Thursday," he is quoted as saying by Sky Sports News.
"It's just been getting used to the new shape and new players. Now the transfer window is closed, that's our squad settled. We've got no excuses now."
Brown recently returned to action for Celtic after starting the season with a hamstring injury.