The Brazilian international will miss the first three games of the Champions League group stage next season.
Neymar was upset that United was penalized at the last minute with the Video Assistant Referee (VAR) system.
Referee Damir Skomina decided that PSG defender Presnel Kimpembe had fired a shot from United's Diogo Dalot in the closing stages of their last 16 Champions League games.
Marcus Rashford scored the resulting penalty, the PSG crashed out of the competition.
Neymar missed the match due to an injury but was present at the Parc des Princes.
"This is a shame, they blame four people who know nothing about football for repeating VAR," Neymar wrote.
"It's just not possible !!! How will a man hold his hand behind his back," he asked, referring to how Kimpembe jumped as he tried to hold Dalot's shot. "Get on your way."
Neymar, the world's most expensive footballer, has just returned to the PSG team following a long break on the sidelines due to a midfoot injury.
PSG will automatically qualify for the group stage of the Champions League next season after winning a second French title in a row last weekend.
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