Referee Chris Foy could not be sure he would have issued a red card had he seen Elliott's alleged kick at the Blackburn player.
Foy did not see the incident during Blackburn's 3-2 win and was asked by the FA to review video footage.
An FA spokesperson said: "The referee said that based on the footage he has seen he cannot say for sure he would have shown a red card.
"Under the rules we are only permitted to take retrospective action if the referee says he would have shown a red card. On that basis we will not take any further action against Elliott."