The last-16 stage of that competition is proving to be a tricky hurdle for the Ligue 1 giants, with an early tumble taken in three successive seasons.
It appeared heading into a midweek meeting with United that a quarter-final spot was PSG’s for the taking, with a 2-0 advantage held from an initial clash at Old Trafford.
Tuchel, who has a star-studded squad at his disposal, has seen questions of his role asked on the back of a humbling exit, but he has the backing of those above him.
Al-Khelaifi told reporters when quizzed on the man at the helm: "I trust Thomas.
"This is not the time for decisions. Decisions require a cool head. We trust him.
"We need to calm down right now and see what the coach wants - that is very important. We are very disappointed with the result and performance. I do not understand.
"We played great at Old Trafford, then we return home and gift them two goals. Honestly, I do not understand that performance in front of our own fans.
"The season is not over. It is a big disappointment, but we still have Ligue 1 and the Coupe de France - we cannot say that this season is now over."
PSG rather shot themselves in the foot against United, with two defensive errors allowing Romelu Lukaku to net twice for the visitors inside the opening half-an-hour.
Al-Khelaifi concedes that Tuchel’s side looked nervous.
While they were able to briefly level after seeing Lukaku open the scoring via Juan Bernat's third goal of the competition, they struggled to produce an attacking spark and eventually fell to a VAR-assisted stoppage-time penalty from Marcus Rashford.
"It is a shock for everyone," added Al-Khelaifi.
"It is serious. Football is not maths - it is not one plus one equals two. After we conceded the first goal, I felt doubt creeping in."