The Brazilian striker scored a 46th minute winner as the Toffees picked up a vital three points against Chelsea.
He celebrated by picking up a blue flare that had been thrown onto the pitch and sent it back into the Gwladys Street End.
No action was taken at the time by referee Kevin Friend, but something could happen retrospectively.
"We will look into the matter but, as far we are concerned, Richarlison was attempting to throw it out of the ground," said an Everton spokesperson.
The consensus from talkSPORT hosts and pundits was that the incident was in the heat of the moment and there should not be any punishment.
Laura Woods told talkSPORT Breakfast: "Let me just give you some context on the Richarlison incident. He picked up a flare and, when we were talking to Martin Samuel [chief sports writer at the Daily Mail] and he was looking at the flares after the match and it looked like they emit smoke rather than being hot or having a flame.
"Richarlison apparently tried to clear it of the ground and ended up going into the fans, or towards the fans.
"The FA and Everton are going to look into it and discuss it as to whether they will take any action or not.
"I remember it was Harvey Elliott who did the same and they contacted him and had a word with him, saying you can't do that.
"Hopefully it's just a slap on the wrist."
Elliott celebrated with a flare at Wembley during Liverpool's Carabao Cup victory over Chelsea on penalties.
The FA wrote to the teenage winger, but no further action was taken.
Former Tottenham midfielder Jamie O'Hara argued that flares should not be in the ground in the first place.
"I don't think he will get banned for three games," O'Hara told talkSPORT. "For one, there shouldn't be flares in the ground anyway. Use your common sense.
"Seeing the moment, I think emotions have got the better of him. I don't really know what he's thinking.
"He's probably in a bit of euphoria and throwing a flare, he's obviously not meaning to do it or harm anyone.
"Don't bring flares into the ground!"
When asked if Richarlison should be banned, ex-Liverpool midfielder Danny Murphy added: "No. You are talking about the letter of the law and if he should be sent off, but you have to put this into context.
"He's celebrating a goal with his own fans in the moment, but he's certainly not meant to cause any harm.
"Ideally, of course you wouldn't want to do that as it could cause some damage."