Dest limped off the field grabbing his hamstring in the 56th minute with Barcelona leading 2-1 on the night and by the same scoreline on aggregate.
"Dest had some discomfort in his hamstring," Barcelona manager Xavi said after the game. "We hope it's nothing serious."
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On Friday, Barcelona confirmed that Dest had suffered a hamstring injury, adding that he would be out for as yet undetermined period of time.
The injury is bad timing for Barcelona, coming just three days before they take on Real Madrid in El Clasico on Sunday (4 p.m. ET; stream LIVE on ESPN+).
The news is also ill-timed for United States men's national team coach Gregg Berhalter.
On Thursday, Dest was named on the U.S. roster for their final three Concacaf World Cup qualifiers later this month but Berhalter suggested he was unlikely to feature.
"It doesn't look good, it doesn't look good, but we're going to get the definitive on the results tomorrow," Berhalter told ESPN's SportsCenter. "But this is one of these things where you're watching these games right before the window and you're holding your breath and hoping guys are going to get through the game healthy and be able to join the team and that's not always the case. We feel bad for Sergino and again this will be a case of the next man needs to step up."
The U.S. are scheduled to take on fierce rivals Mexico at the Estadio Azteca on March 24 before hosting Panama (March 27) and traveling to Costa Rica (March 30) to round out their "Octagonal" campaign. After 11 of the 14 rounds of games, the U.S. (21 pts) sits in second place in the standings, level on points with third-placed Mexico and four points ahead of fourth-placed Panama.
The top three teams will qualify automatically for the 2022 World Cup in Qatar with the fourth-placed team facing an intercontinental playoff.
Dest has been a mainstay of late for the U.S., starting in six qualifiers during this cycle.
ESPN's Samuel Marsden contributed to this report.