Ferran Torres hit a hat-trick, while Roony Bardghji also scored a first goal for the club.
Flick said afterwards: "I think the first half was very good, but we were tired in the second half. Defensively, we weren't able to control the final minutes of the game. But I want to be positive in my assessment, although we'll analyze it.
"The important thing is that we won. I'm very happy with the team. I respect how we fought and came back. The players were exhausted at the end. They fought for 90 minutes. I really value what we did today.
"It's always very important to score two goals so close together and win, and it's not easy against a team like Betis, which is very technical and high-quality, and has fantastic players."
On Torres, Flick continued: "Ferran is a very intelligent player. He knows how to read space very well and he did so fantastically well today. He has the right mentality and confidence. This is the way forward.
"He deserves to be in the starting eleven. He's always there when needed. This stadium is Ferran Torres Stadium, even when he plays for the national team, where he also scored a hat-trick."
On Rooney, he added: "He gives us more options to choose from, and that's good. Everything I've seen from him I've liked. He's linked up well. He's tracked back, he's worked hard defensively. He's growing and improving. He's a fantastic player."