An investigation has been opened by French border police and on Thursday evening PSG released a statement.
Around 30 supporters, furious about the team's defeat, were waiting for the Paris players as they emerged from Le Bourget airport outside the French capital in the early hours of Thursday morning.
In chaotic scenes, Italian international Motta's car accelerated as supporters and photographers obstructed the road. One man banged on his vehicle and was struck by the car.
He was taken to hospital but his injuries were minor, a police source told AFP. The injured fan later filed a formal complaint over the incident.
An investigation has been opened by French border police and on Thursday evening PSG released a statement in which they hit out at the behaviour of some of those who greeted them at the airport, while defending Motta.
The club said their players "were confronted at Bourget airport by several individuals, despite the club and authorities reinforcing security.
"These individuals verbally insulted the players before vandalising their cars. Several vehicles were damaged.
"In this extremely hostile and aggressive climate, all vehicles were escorted to ensure the safe passage of the players, their families and club staff members.
"One individual was struck by a car trying to escape the crowd that was physically threatening the players and their families."
PSG added that they had "informed the investigators of their readiness to help the investigation, to get to the bottom of this regrettable incident."
Earlier, the Paris Ultras Collective (CUP) supporter group insisted they were not to blame for the chaos, stressing they had "nothing to do with what happened at Le Bourget airport upon the team's return".
"We're not those who give back their jersey at the first sign of difficulty. Like we have always been, we are behind the club, the president, the coaching staff and the players to lift titles and cups, then come back stronger next season," the group said in a statement sent to AFP.
The 6-1 defeat by Barcelona at the Camp Nou and the exit from the last 16 of the competition was a historic defeat for Qatari-owned PSG after they had won the first leg 4-0 in Paris, and has cast doubt over coach Unai Emery's future at the club.