Niasse scored Everton's second equaliser in the 2-2 draw at Selhurst Park.
"Everton's Oumar Niasse will serve a two-match suspension with immediate effect after his denial of an FA charge of 'Successful Deception of a Match Official' was rejected," the FA said.
The Senegal international will miss Everton's games at Southampton on Sunday and at home to West Ham United on Nov. 29.
Everton caretaker manager David Unsworth believes Niasse was fouled by Dann and said the FA's charge could set a dangerous precedent for debatable decisions in the future.
"He (Niasse) was shocked and I was shocked," Unsworth told a news conference.
"My view won't change. Contact is contact. Anywhere on the pitch, it's a foul. I think these people will be very busy if that's going to be the case. You will have to look into every foul across the board.
"It's a dangerous precedent that could be set if decisions go against you that are debatable."
The new law allowing retrospective punishment for simulation was introduced in May.
While Niasse is the first Premier League player to be suspended under the law, Bristol City defender Bailey Wright was banned for two games this month after being found guilty of simulation in an off-the-ball clash with Fulham's Aboubakar Kamara during a Championship (second-tier) fixture.
Aboubakar was initially shown a red card after Wright fell theatrically to the ground but it was later rescinded.
(Reporting by Hardik Vyas in Bengaluru; Editing by Ken Ferris and Toby Davis)
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