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Everton have had two appeals against midfielder Allan's red card in the 1-0 win over Newcastle rejected.
The Brazilian was shown a yellow card by referee Craig Pawson after bringing down Newcastle's Allan Saint-Maximin.
But, after the video assistant referee (VAR) told him to review the foul on a monitor, Pawson upgraded it to red.
Everton said their "request to overturn that decision was rejected" along with "a second appeal to downgrade the ban for excessive punishment".
Allan will now miss the Goodison Park club's FA Cup quarter-final against Crystal Palace on Sunday, and Premier League games at West Ham and Burnley.
Everton received an apology from referees' chief Mike Riley this season after they were denied a penalty during a 1-0 defeat by Manchester City last month.
On that occasion the VAR did not tell referee Paul Tierney to reconsider his decision.
Prior to the appeal being rejected by an independent regulatory commission, Toffees boss Frank Lampard said: "We don't need an apology, but just to look at the decision in hindsight and was it enough to warrant a red card? Absolutely not.
"Sometimes our emotions are wrong, but in the cold light of day that's not a red card. We don't want to lose Allan for three games and now we're in their hands."
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