The foot up and studs showing challenge, labelled “criminal” by Chelsea boss Jose Mourinho, in the 70th minute of Saturday’s 1-1 draw resulted in Matic’s sending off for lashing out angrily.
While the Serbian midfielder was dismissed, Burnley forward Barnes went unpunished by referee Martin Atkinson and the Clarets took advantage of their numerical advantage to snatch a late equaliser.
Having initially gone to ground in pain, Matic ran towards Barnes and bundled him to the ground, earning the red card.
Chelsea are reportedly set to appeal against Matic’s three-game ban, but Mourinho had also suggested that action should be taken against Barnes, who was not even cautioned.
But the FA revealed on Twitter that it would not be punishing the Clarets forward, and explained the rationale over five posts.
They read: “In the vast majority of challenges for the ball, no retrospective action is taken as the incident has been seen by the match officials.
“Retrospective action introduced as deterrent for ‘off the ball incidents’ (e.g. kicks, stamps etc.) committed out of sight of officials.
“Whole game in agreement that, in vast majority of cases, match officials are best-placed to deal with incidents to avoid re-refereeing.
“In line with this rationale, FA confirm no further action in relation to Ashley Barnes as incident was seen by the officials.”