Gareth Southgate's men were defeated by Italy during a nail-biting penalty shootout at Wembley on Sunday.
Luke Shaw fired England into the lead in the opening two minutes, but Leonardo Bonucci pulled back a second-half equaliser for Italy to send the final to extra time.
However, Chiellini lost the ball in injury time and was caught dragging Saka back with a handful of his England shirt.
The 36-year-old Italy captain was handed a yellow card by referee Bjorn Kuipers, despite fans claiming that Chiellini should have been sent off.
Now, Change.org user Custard Cream claimed the match was "not fair at all" and alleged that the match officials were "biased" in favour of Italy.
The petition's description reads: "The match on 11/07/2021 was not fair at all. After Italy only receiving a yellow card for dragging England players like they were slaves.
"All the pushes, pulls and kicks and Italy [were] still allowed to win? Definitely biased.
"Italy should have been given a red card for their gameplay and the rematch should happen with a non-biased referee. This was not fair at all."
Saka, along with Marcus Rashford and Jadon Sancho, missed from the spot-kick as England's hopes of lifting major silverware for the first time since 1966 were dashed.
However, the England trio were subjected to vile racist abuse on social media after England's defeat to Italy in the final.
The Football Association blasted fans who targeted Rashford, Saka and Sancho with horrific messages, saying it will do "everything we can to stamp discrimination" out of football.
Southgate insisted that his England players "should be incredibly proud of themselves," despite their defeat to Italy in the Euro 2020 final.
The England manager said: "Tonight is going to be extremely difficult for all of us, of course.
"You have to feel that disappointment because the opportunities to win trophies like this are so rare in your life.
"But when they reflect on what they have done, they should be incredibly proud of themselves.
"The players have been an absolute credit. They have given everything they possibly could.
"They have been an absolute joy to work with and they have gone further than we've gone for so long. But it is incredibly painful in that dressing room."
Featured Image Credit: PA
- ‘I Grabbed Him Good!’ - Giorgio Chiellini Laughs As He Recalls Shirt Pull On Bukayo Saka In 2020 Euro Final
- Bukayo Saka shone in first tournament game since Euro 2020 penalty miss
- Bukayo Saka surprised a young fan who gave him his pocket money after Euro 2020 final
- Jose Mourinho Praises Giorgio Chiellini For Cynical Foul On Bukayo Saka In Italy's Euro 2020 Win