PSG have spent a fortune on assembling a team capable of winning Europe's elite club competition, but have failed to get past the quarter-final stages since being taken over by big-spending Qatar Sports Investments in 2011.
"I'm very disappointed with the result and the game. I don't understand how we lost," Al-Khelaifi said. "We won 2-0 there. Here in Paris we lost 3-1. We gave them everything to win. It was easy for them. I don't understand."
PSG appointed Tuchel in May in the hope the uncompromising German would further their quest for European glory, and Al-Khelaifi said the club would not take any decisions over his future in the heat of the moment.
"I trust the coach... but it's not because we lose a match that we have to act now," the president was quoted as saying by French sports newspaper L'Equipe.
"We must make decisions with a cool head but this is not the moment. We want to calm down."
The defeat sparked emotions ranging from anger to despair from members of Tuchel's squad.
Brazil international Neymar, who was injured for both legs, lashed out at the video assistant referees system after United won a late penalty.
His compatriots, club captain Thiago Silva and Marquinhos, offered a more measured perspective, stressing the need for the team to reflect on the defeat.
"We have to go away and think, like we do every year," Marquinhos said. "We have to think about what's working and not working so that we can come back stronger."
Silva asked the club's fans for forgiveness.
"It's difficult to speak. It's a shame," he said. "We were on a good run and yet again it ends here. That's football. Nothing worked today. I ask our fans to forgive us."
(Reporting by Shrivathsa Sridhar in Bengaluru, Editing by Simon Jennings)
