It was PSG's heaviest league defeat since Qatar Sports Investment (QSI) took over the club in 2011.
As a result, PSG missed the opportunity to be crowned Ligue 1 champions, and Mbappe, who had two goals disallowed in the first half, has since stated that the loss was unacceptable.
World Cup victor Mbappe had already had one goal chalked off by the officials when a comical Meunier own goal set Lille on their way after six minutes.
However, the Spanish full-back was shown a straight red card shortly before the break when he brought down Pepe as the striker was rushing towards goal.
Attacker Pepe slotted home Lille's second five minutes after the break when he latched onto a superb Jonathan Ikone through ball and after that the floodgates opened.
Mbappe tormented the Lille defence but he was isolated up front and it was Lille who scored another, in the 65th when Bamba out-paced the defence and beat goalkeeper Alphonse Areola.
Headers from defenders Gabriel and Jose Fonte turned it into a rout.
He told reporters: "It's too much, we miss so many players, it's not possible like that".
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"We're going to be champions but we can not lose like this", the 20-year-old Mbappe added.
"But we must play with more personality".
"We will be 13 or 14 players short".
Tuchel only had six substitutes on his bench for the 5-1 defeat.
"Moussa Diaby has played only twice and (Thilo) Kehrer is sick - ordinarily they should not be with us, but here we are".
"There are 18 points left to play for - so I will let my players enjoy this for 48 hours, even if they have training on Monday", said a delighted Christophe Galtier. "To win here, we would have needed more quality".
"Marquinhos is sick, Thiago Silva is injured".
"Yes, I will be telling the president as this situation is not good".
Earlier, Saint-Etienne kept the pressure on Lyon and Marseille in the race for third spot with a 3-0 home win against Bordeaux.
St Etienne have 53 points, three behind third-placed Olympique Lyonnais, who occupy the final Champions League qualifying spot.