The home crowd spilled onto the pitch moments after Phil Jagielka's penalty miss had knocked the Premier League side out of the Carling Cup.
It was then that Moyes claims to have seen a Brentford fan launch a bottle into the Everton supporters' end.
The FA are keen to follow up Moyes' claim although it is understood that a full investigation is not being considered at the moment.
An FA spokesperson said: "We are aware of the claims made by Mr Moyes last night and have contacted Brentford to ask for their observations into the matter."
Moyes was left fuming at the alleged incident, with the Scot having to hold himself back from confronting the person he claims was responsible.
The Everton boss said: "I saw a fan throw a bottle into our supporters. It was terrible. I said to him 'I saw your face. I saw who you were'.
"He got a bottle and went right up and threw it right into the middle of our supporters."
Moyes also criticised the decision to hold the penalty shootout, which Everton lost 4-3, in front of home supporters.
"I think the police decided to take the penalty kicks at the end for security reasons. That proved to be a right bloomer, didn't it?" he fumed.
"If the police want me to follow it up and try to find the individual that threw the bottle into the crowd then that would be fine by me, it wouldn't be a problem," he continued.
"I didn't grab him. I wanted to but obviously that would have brought more attention to the situation."
Brentford are expected to issue a press release about the allegation on Wednesday afternoon.