Barca drew 1-1, with Lamine Yamal's first-half penalty canceled out by Rayo's Fran Perez after the break.
An unimpressed Flick said afterwards: "A point is fine. We didn't deserve more. We made a lot of errors. There were a lot of mistakes. It wasn't a good game. We have to do better.
"If everyone has a good attitude, we'll do better..." he continued. "The most important thing for me is that when the transfer window closes, everyone is 100 percent committed. It's important not to have egos; they kill the chances of success.
"I've spoken with the players. Almost all of them are leaving with their national teams, and I've spoken with them about the match now. I'm happy there's a break; we'll work on our mistakes. With a good attitude, we'll do better."
Asked if Barca are now relying on Yamal, the German also said, "No, he's a key player, just like any other. After the break, we'll have worked harder and we'll do better."