Matic was sent off in the 70th minute at Stamford Bridge for his violent reaction to a studs-up challenge from Burnley’s Ashley Barnes.
But the FA said on Twitter on Monday that no action would be taken against Barnes as the incident was seen by the officials.
“A criminal tackle. Matic is a very lucky guy,” said Chelsea manager Jose Mourinho after his midfield player escaped injury.
The 26-year-old Serbian international rushed at Barnes and pushed him to the ground but he was defended by his manager.
“Football is about emotions and clearly Nemanja Matic had a reason to lose his emotions,” Mourinho said.
“What are the consequences of his push? Nothing. The consequence for Matic from the tackle? It could have been the end of his career.”
The FA added on Twitter: “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’ (for example 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.”
Chelsea must submit their appeal to the FA by 1300 GMT on Tuesday. Unless it succeeds, Matic will miss Sunday’s League Cup final against Tottenham Hotspur at Wembley.
He will also be banned for Premier League matches against West Ham United and Southampton.
(Reporting by Mike Collett, additional reporting by Ken Ferris; editing by Tony Jimenez and Justin Palmer)