Wanyama scored the opening goal before Tony Watt doubled the Hoops' advantage against the Catalan giants.
The Kenyan giant was instrumental in Celtic's midfield and believes that Celtic's ability to ease pressure with spells of possession proved vital.
He told Sky Sports News: "This is unbelievable. Today we just worked hard, we were good as a team, compact and got the three points.
"I cant describe it, we're very glad it's unreal, we beat one of the best teams in the world. It's always important when you're playing this team to keep the ball and today we were very good, calm with the ball. That kept us in the game.
"We've been working hard at set pieces and knew we'd get one. We did it well. I'm so happy for the team, we did well tonight."
Victory over Barca keeps Celtic second in Group G, three points clear of Benfica ahead of their trip to Lisbon in three weeks' time.