Upon their return to Paris, the club alleges the travelling party were verbally abused and several vehicles damaged at Bourget Airport, while club staff, players and their families had to be escorted from the scene.
"On Wednesday night... the Paris St Germain players were confronted and threatened by several individuals at Bourget Airport," PSG said on its website (www.psg.fr/en).
The club added that the crowd was "physically threatening the players and their families".
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"A police investigation is underway to establish exactly what happened... The Club strongly condemns the actions and behaviour of the individuals in question."
Barcelona became the first team in Champions League history to overturn a four-goal deficit in a knockout tie, with the feat being hailed as the greatest ever comeback in the tournament.
Several PSG players apologised to fans in the wake of the defeat, which club president Nasser al Khelaifi described as a "nightmare".
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
