Two-goal hero van Persie said victory would go some way to making up for Saturday's shock defeat to Hull City.
He told ITV1: "After Saturday we were disappointed and today was a good day to make it up and make it right.
"It was a good game and good spirit from all of us and we deserved the win."
Despite the European masterclass from his team, van Persie insisted Arsenal are not yet the finished article.
"It's still early - it's only the second game," he said.
"It shows a little bit that we can play but we knew that before.''