Fermin Torres struck a hat-trick, with Marcus Rashford scoring twice on the night. Lamine Yamal also converted a penalty for the Blaugrana.
Afterwards, Flick stated: "At the beginning of the game we had some problems but we deserved the victory. Every goal and every victory is important."
On Torres, he said: "His performance has been sensational. Three goals, the first very important, gave us confidence. It has it all: it's dynamic, it has speed..."
"He has great potential, his dynamic will be different now, he positions himself well... The first two goals were especially important for us."
Flick also had a word for Manchester United loanee Rashford, saying: "I have played a very good game. He's performing very well. He's an important player on the pitch.
"The penalty was a penalty, and the second could be too. What I expect from him, he gives 100 percent. It's important for me to have him. He's quick on the ball, he combines, he's good in front of the box... as he gains confidence and plays more with his teams, he'll get even better."