Barca won 2-0 thanks to a Raphinha penalty and a Lamine Yamal goal, as Villarreal lost defender Renato Veiga to a red card midway through the first-half.
Flick said afterwards: "The victory is important. Villarreal has a great team, they have a lot of speed up front. I'm happy with the three points.
"I'm happy for the players; we won the three points against a great team. I liked how they played. They're good, attacking players. In the end, the important thing is the three points and that we kept a clean sheet. I'm happy with the three points."
On their eight-game winning streak, he also said: "It's good, and I think the quality, mentality, and attitude have been fantastic. That's what I see in training. What I see in the sessions is fantastic, and that shows in the matches.
"We have a lot of quality. Today wasn't an easy match defensively; the players are tired. They need to rest. But I want to highlight the team's attitude and mentality; it's very good to see."
Flick also stated: "Joan García helped us a lot today with his saves. He's an important player for us. But the whole team tries to defend and help.
"We work as a team. The team was tired and the passes weren't as precise, but it's okay. My players can rest now."