Former player Achraf Hakimi opened the score before Wonderkid Desire Done took a brace to put PSG out of reach.
Khvicha Kvaratskhelia and the 18-year-old Senny Mayulu completed the route and earned PSG their first Champions League title and the greatest definitive victory in the history of the competition.
Despite bringing inter to the final, Inzaghi, 49, is strongly connected to a move to Saudi Arabia with Al-Hilal prepared to make him the best-paid manager in the world.
In the press after the game, Interpresident Beppe Marotta said that the defeat would not influence their decision about the future of Inzaghi.
He said: “Absolutely no evaluation change. We have already said that we would meet Initaghi next week.
“He still has a year on his contract and has proven over the past four years that he definitely deserves to be here and many of our achievements have been to him today.”