Ten players from the starting eleven, excluding Brown, made their European top flight debut in the scoreless draw with Benfica at Celtic Park and the midfield general was extremely proud of the work his teammates did to secure a point.
"I think overall we were the better team," Brown told Sky Sports HD3.
"They didn't show it was their debut, that's for sure. They were unbelievable, they were calm under pressure."
Brown added: "We didn't create as many chances as we'd like but I think we played really well."
Celtic's next Champions League mission is against Spartak Moscow in Russia on October 2 but prior to that they take on Dundee in the league on Saturday followed by Raith Rovers in the League Cup on Tuesday and and a trip to Motherwell next weekend.