Paqueta was dismissed late in the game at the London Stadium after receiving two yellow cards in quick succession for dissent.
The Brazilian was cleared of four spot-fixing charges by the FA earlier this year following a lengthy investigation.
"It's ridiculous to have your life and career affected for two years without any psychological support from the federation," Paqueta posted on X.
"Perhaps this ridiculous behaviour is just a reflection of everything I've had to endure and, it seems, have to continue enduring! I'm sorry if I'm not perfect."
Paqueta's post was in reply to a Sky Sports post that included footage of the incident with the comment "It's ridiculous behaviour."
The 28-year-old also posted an apology to teammates and fans, but argued his actions did not warrant a dismissal.
"I understand that now I have to look like the villain, it's difficult to live with everything that has been caused in my life and in my psyche!" his translated Portuguese post said. "I will continue trying to prevent them from affecting me even more.
"This does not justify my expulsion and for that I apologize to the fans and my teammates!"
Paqueta was cleared on July 31st of charges alleging he had deliberately sought to receive a booking during four Premier League games between November 2022 and August 2023 against Leicester City, Aston Villa, Leeds United and Bournemouth.
Paqueta, who was facing the risk of a lifetime ban, denied the alleged spot-fixing charges.