Mauro Icardi and Neymar scored - the Brazil international's 18th successful penalty from the 19 he has taken for PSG - for the Ligue 1 champion, while Dimitri Payet set up a tense finale with an 89th-minute strike for Andre Villas-Boas's side.
PSG held on, though, to claim a record eighth consecutive Trophee des Champions crown and their 10th overall midweek.
It was only Pochettino's third game in charge of PSG and the former Tottenham boss made sure he recognised the work of Tuchel, who was dismissed as head coach on 29 December.
"I want to thank the players, Leonardo [sporting director] and Nasser Al-Khelaifi [president]," Pochettino – a Champions League and EFL Cup runner-up with Spurs – said. "I also have a thought for Thomas Tuchel and his staff, who allowed us to play this match."
"We are making progress in all areas where we want to implement our ideas. We have a very intelligent group of players, with great adaptability. We are very happy.
"I hope to win other titles, but the first one will always be special.
"The group has shown a lot of maturity, it has learned from its mistakes. It's a huge emotion to win with this staff, it's difficult to describe in words, especially since it's a club that made me become a better person, a better player."
Marseille finished the game having had four shots on target to PSG's three, although the Parisians enjoyed a whopping 63.6 per cent possession and completed 268 more passes than their opponent.
Despite that, Villas-Boas believes his side did not deserve to lose.
"It was a balanced game, with few chances for both teams," he said. "We were the best team. I think we didn't deserve to lose this game. PSG going 2-0 up went against the run of play
"Congratulations to PSG. The best honour they gave us was the party that followed, because we offered them a difficult match."