Barca suffered injuries to defenders Jules Kounde and Alejandro Balde during their 3-0 win over Atletico Madrid in the Copa del Rey semi-final on Tuesday, a result that was not enough to overturn a four-goal deficit from the first leg.
Midfielders Frenkie de Jong and Gavi also remain sidelined, but striker Robert Lewandowski is fit for the Athletic clash.
"These things happen. I'm not happy," Flick told reporters on Friday.
"We have to talk about what we can improve. That is always my responsibility. It's not on the medical staff or the physios - it's my responsibility.
"I want to talk to the doctors, the physios and the technical staff to see what we can do better. It's about managing the team, and it's not pleasant, especially at such a crucial moment.
"But we're optimistic. This gives other players the opportunity to show how good they are."
Real's shock 1-0 home loss to Getafe on Monday left leaders Barca four points clear after 26 matches. Athletic sit ninth.
"There's still a long way to go until the end of May. There are many games left. On Tuesday, we had two more injuries... We have to deal with it and move on. We need to stay optimistic about the things we can't change," Flick said.
Although Barca failed to reach the Copa del Rey final, Flick said he took plenty of encouragement from their performance.
"In the end, it wasn't enough, and we have to accept that. But my feeling is that we are at a very high level - and that should give us confidence," the German added.