Everton will contact the Professional Game Match Officials Limited (PGMOL) to query why a challenge they feel should have led to a penalty was not reviewed further in the Merseyside derby.
With the game goalless, forward Anthony Gordon went over in the area following a challenge by Liverpool's Joel Matip.
Eight minutes after the incident Andy Robertson scored Liverpool's opener with Divock Origi sealing the 2-0 win.
The defeat left Everton in the relegation zone with six games to go.
Frank Lampard's side are two points below Burnley, who occupy the final position of safety, though the Toffees have a game in hand.
Lampard suggested post match that a penalty would have been given if the challenge had been made on a Liverpool player.
"It was a penalty, you don't get them at Anfield," he said.
"If that was Mohamed Salah at the Kop end, I think [the referee] gives that. It was a foul on Anthony."
The FA have written to Lampard asking him to explain his post-match comments about referee Stuart Attwell. He could face a charge if found to have questioned the official's integrity.
Earlier this season PGMOL apologised to Everton after they were denied a penalty in their 1-0 defeat by Manchester City despite midfielder Rodri appearing to use his hand to control the ball.
Both Everton and Liverpool have also been warned about their future conduct, but avoided any charges, following a melee when Toffees midfielder Abdoulaye Doucoure was booked for kicking Fabinho. It came after play was allowed to continue despite Richarlison lying on the ground injured.
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