The 21-year-old was dismissed in stoppage time during the Magpies' 2-1 home defeat on Saturday after taking a wild swing at Fagan, who was left with a fractured left leg.
But the FA confirmed on Wednesday that it can take no further action on top of a mandatory three-match suspension for the red card.
A spokesman said: "Every sending off carries an automatic sanction under the current regulations.
"The FA doesn't have the power to extend automatic suspensions.
"The only circumstances in which we could take any further action would be to issue an additional charge against a player.
"This occurs only in exceptional cases, such as Ben Thatcher's challenge on Pedro Mendes in 2006."
However, the FA spokesman also confirmed that an ongoing review of their disciplinary procedures could see a sliding scale introduced to increase punishments for serious offences.
He said: "We are currently reviewing disciplinary procedures with a view to potential changes for next season and a sliding scale for red-card offences is one of the options under consideration."