- Tag results for Neymar
Klopp insisted Neymar wasn't fully fit in Russia after breaking a bone in his foot in February that forced him to miss the rest of the club season with the French giants before the World Cup.
PSG's second goal arrived just after half-time, with Cavani converting a penalty, his third goal in as many games this season.
Neymar gave Brazil the lead from the penalty spot in the fourth minute on Tuesday after Richarlison was brought down by Roberto Dominguez at FedEx field.
Brazil, playing their first international since a disappointing World Cup quarter-final exit, were in complete control throughout a low-key encounter at the MetLife Stadium in New Jersey.
The forward, who led the team in the 2018 FIFA World Cup, has been frequently targeted by critics for his behaviour on the field.
It is an intriguing move, and a world away from the blockbuster deals of August 2017 when PSG committed the two biggest transfer fees in history to sign Neymar and Kylian Mbappe.
The Brazilian, who scored as PSG beat Angers in Ligue 1 on Saturday, was on a flying visit to Spain.
Gianluigi Buffon also produced a couple of sharp saves on his home bow in goal for PSG as coach Thomas Tuchel made a winning start at the Parc des Princes.
Tuchel insisted that Neymar is the "key player" for his side, as his team prepare for the start of their Ligue 1 title defence against Caen on Sunday.
Neymar returned in time for the World Cup, but failed to inspire Brazil to a record-extending sixth title as they suffered a 2-1 quarter-final loss to Belgium.
Angel Di Maria's double fired PSG to their first silverware under new coach Thomas Tuchel as Neymar, long sidelined by a metatarsal fracture, came on as a late substitute.
The world's most expensive player, wearing a canary-yellow hoodie, posed for pictures with airport staff before his noisy welcome in the arrivals hall.
Neymar in an ad admitted that he sometimes exaggerated his reactions after being fouled at the FIFA World Cup.
In 2011, Neymar was criticized for constant misbehavior and he used an advert sponsored by phone carrier Nextel to address his fans.
The Brazilian superstar was widely lambasted in Russia for his theatrical reactions to challenges which often left the world's most expensive footballer wincing and rolling on the ground.