Following the 5-1 humbling, Kylian Mbappe suggested the defeat was due to a lack of personality rather than squad depth, adding that the club's mental fragility has been an ongoing theme across the campaign.
PSG went behind early on a Thomas Meunier own goal, as well as having a pair of goals ruled out for offside, though were level through Juan Bernat midway through the first-half.
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.
Pepe finished off a one-on-one and Jonathan Bamba smashed in at the near post to put Lille in control.
Lille's Jose Fonte and teammates celebrate after the match.
"With 10 players it became complicated, we played with sick players who should not have played".
Pepe was denied by Areola before Dani Alves made a crucial intervention as Loic Remy went for goal, but it would still get worse for the champions as ex-Southampton defender Fonte headed in Pepe's corner for a fifth.
"We lack personality, it's one of our flaws, we have to correct this".
"Today we played like amateurs".
PSG played the match with a number of notable absentees, including Neymar, Edinson Cavani and Angel Di Maria.
"Of course, losing to 5-1 was normal, given the circumstances", said Tuchel.
"Even [Moussa] Diaby and [Thilo] Kehrer could not play I do not know who can play in Nantes!"
But Tuchel took umbrage to the comments after the match and has since played down suggestions of any psychological shortcomings from his squad, instead commenting that he was forced to utilise "sick players who should not have played".
"We are missing too many players, and nobody is speaking about it".
They fell behind after just seven minutes when Thomas Meunier put the ball in his own net.
"Nobody said anything before because we were winning". Everyone sees that. And I will tell that to the president, yes.
Earlier on Sunday, Saint-Etienne closed in on Champions League football after Mathieu Debuchy scored twice in a 3-0 win over Bordeaux that moves them to within three points of Lyon.