Lamine Yamal (2), Dani Olmo and Pedri struck for the visitors, with Cristhian Stuani netting late for Girona.
Flick said: "The season has just started. We played very well, focused, concentrated... we knew that if we gave them space we could combine. We pressed very well. The first goal was incredible. Very beautiful. We deserved the victory. It was a tough game. Girona plays very well. But we started very well and I think we deserved the victory.
"We have trained very hard, we prepare well for each game. We have to take it step by step, game by game, but we want to win. We are in a good moment and we have to keep going. We can't stop. When you start, you want to win because it gives you confidence.
"In the first few minutes we saw that we are a compact team. We trust in ourselves. We did well. We had chances, today, to score even one or two more goals. I am very happy with how the team played."
On Yamal, he added: "He made the difference, he presses very well and that's very important. It's important that everyone presses high. That combination of talent and pressure is very good for us. Lamine played very well and we finished the chances we had well."