Dani Olmo scored twice, with Raphinha also netting as Barca went 3-0 ahead in the first-half. Javi Puedo scored for Espanyol after the break.
Afterwards, Flick admitted he was pleased with the points on the day.
Second-half:
"We lost a lot of balls in the second half. I didn't like the way we played. I'm very happy with the three points, the derby is always complicated.
"I'll play with six players, they're all very good, that's not a problem. I'm very happy that they're coming back and because of Dani's performance today. I'll gradually reduce the minutes, to avoid possible relapses.
"I'm satisfied. It's three points. It was a derby. I'm happy with the result and the three points. We lowered the intensity in the second half, we had less attention and concentration... Ansu scored and it was disallowed. In the second half, we dropped the ball.
"We prepared very well for all the teams. I'm not afraid. I trust the team. They're doing well. They have to show it on the pitch. The fans are very happy with how the team is playing and that's how it should be."
Dani Olmo:
"He knows how to score. He was very important today. And Fermin, who played against Bayern and Real Madrid. We are very happy that Dani is back, even though he is not 100 percent.
"In the second half, I didn't want to make too many changes. We lost concentration a bit. We made a lot of mistakes. I like to change players, I like to keep the goalscorers. But I wanted to take on Gavi, Fermin, Frenkie de Jong... We had two left, I could have made one more earlier.
"After a long injury, it's normal. He plays 60 minutes and at half-time I told him I would change him and Casadó."
Ferran Torres:
"I understand it perfectly. It's normal when he said that he wasn't fit. There are things that are much more important than football. It's normal."
Frenkie de Jong:
"He can play with Marc Casadó and others. There's no problem. He's a '8' player, but he can play as a '6' too. It wasn't easy for the players who came in. There wasn't the same concentration and we made mistakes."