Sheraldo Becker hit the winner for La Real, with Robert Lewandowski having a first-half goal for Barca denied by VAR for offside.
Flick later said, "I think the goal that was disallowed was the wrong decision. Today wasn't our day. We made bad decisions in attack. We have to accept that.
"Regarding Lamine (Yamal), the doctors will contact the Federation, but he couldn't play today. The Federation will make the right decision. I've been in that situation, and I think that as a coach they can decide and we have to accept what they decide.
"I wasn't very angry (with the referee). Just a little. I told him it was a goal and it was a wrong decision. It wasn't offside. If it had been valid, it would have been a different game for us. It wasn't our day."
He added, "I think the responsibility for the defeat is ours, we could have played much better. We were good in the first 15 minutes. It is a defeat, but the games so far have been fantastic. I value what the team has done. We finished the game together. But we couldn't win, we weren't strong enough."