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 was fit for the Athletic clash.
"These things happen. I'm not happy," Flick told reporters.
"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.
"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.