The fourth division club fought valiantly until Turkey striker Mevlut Erding finally broke the deadlock in the 53rd minute by heading home the winner.
PSG, who have lifted the Cup seven times, will face Monaco in the final. The principality team advanced by beating Racing Lens 1-0 after extra time on Tuesday.
Quevilly had knocked out Ligue 1 sides Stade Rennes and Boulogne on their way to the last four and so confident were their fans of pulling off another shock win, many of them had already bought tickets for the May 1 finale at Stade de France.
However, the dream ended on Wednesday.
"I guess PSG deserved to win because they are a lot more powerful than we are," Quevilly coach Regis Brouard told reporters.
"I wish to congratulate my players for what they have accomplished. I'm really proud of them."
His PSG counterpart Antoine Kombouare paid tribute to the amateurs from Normandy, saying: "We knew we had to respect Quevilly and they showed why tonight by giving us a hard time.
Quevilly, a side from a Rouen suburb, hosted PSG in Caen, 120 kilometres away from their home, because their own stadium did not meet safety standards.
PSG fans were banned from attending after the Ligue 1 side, who have been struggling for years to keep their most violent supporters under control, decided to stop selling tickets for away games until the end of the season.
Some 800 police were on duty. No incidents were reported around or during the game, attended by a 21,000 partisan crowd, roughly the Quevilly population, clad in yellow and black, the club's colours.
As a third division team, Quevilly had lost the 1927 final to Olympique Marseille and a semi-final to Girondins Bordeaux in 1968.
