“Everyone deserves congratulations, everyone who came off the bench, everyone who was involved in the match,” Neymar said.
“It was great, the first of many, let’s go!”
The victory, PSG’s ninth Super Cup in the past 10 years, comes after Galtier was appointed as their new boss in early July.
Galtier dedicated the victory to predecessor Mauricio Pochettino who led PSG to last season’s Ligue 1 title.
“Of course I’m very happy, for the players, for the hard work that we put in during pre-season,” Galtier said.
“If we are here it’s because the team won the league last season with a different manager who contributed to this trophy.
“I’d like to dedicate this to Mauricio Pochettino because the team won the league because of him.
“Of course it was important to bring this trophy back to Paris and I liked the way the team played for the whole game even though we conceded a chance.”