Brown is one of a number of young to feature in the Glasgow pack this season alongside fellow 22-year-olds Max Williamson, Euan Ferrie, Gregor Hiddleston and 21-year-old Alex Samuel.
"It's such a positive culture here, the coaches and other players feed you with confidence," Brown told the BBC Scotland website. "There's a lot of boys getting opportunities and the way that we train sets boys up for that.
"When it comes to game time, it's not that much of a step up. People are going in there with the confidence just to play the game that they've always been playing."
Brown started both of Glasgow's recent games in South Africa in the second-row, although he sees himself as primarily a back-row player.
The match against the Lions was his fifth start of the season after an injury-interrupted campaign.
"At the start of the season I was really pleased to build a run of games and then I picked up an injury in that away game at Bayonne, which knocked me out for a few months," he added.
"It was pretty tough dealing with that, but to come back at the tail-end of the season and get some game time in some pretty big games has been huge for me. I've really enjoyed it and it feels like I'm getting back to where I was."