Defenders Jules Kounde and Alejandro Balde both suffered hamstring injuries during the second leg at Spotify Camp Nou on Tuesday night. Both players are expected to miss around a month, leaving Barcelona short of options at full-back during a crucial period of the season.
Barcelona produced an impressive performance to beat Atletico 3-0 in the second leg, but the result was not enough to overturn the first-leg deficit. Diego Simeone's side still advanced 4-3 on aggregate despite the defeat in Catalonia.
The injuries now leave Flick without his regular full-back pairing at a time when the schedule is becoming increasingly demanding.
Joao Cancelo is capable of playing on either side of defence and is expected to take on a bigger role in the coming matches. Eric Garcia and Gerard Martin could also be used as emergency options, although both have mainly featured in central defensive roles this season.
Flick has also turned to the club's academy for extra cover. Nineteen-year-old left-back Patricio Pacifico trained with the first team this week and could be included in the squad for the upcoming league match against Athletic Club at San Mames Stadium.
Pacifico joined Barcelona during the January transfer window from Uruguayan side Defensor Sporting and has been playing for Barcelona Atletic since his arrival. His chances of stepping up have increased after La Masia defender Jofre Torrents suffered a season-ending ankle injury.
Barcelona's next two fixtures will test Flick's depleted defence. The Catalan club travel to face Athletic Club in La Liga before turning their focus to Europe.
Barcelona face Athletic Club on Saturday, 7 March in a La Liga Matchday 27 clash at San Mames. Just three days later, they travel to St. James' Park to face Newcastle United in the first leg of their UEFA Champions League Round of 16 tie on Tuesday, 10 March.
With limited defensive options available, Flick may have to rely on squad depth and young players as Barcelona look to stay competitive in both domestic and European competitions. Pacifico is likely to start on the bench in Bilbao, but the young defender could be called upon if the injury crisis deepens.