The Toffees gave up a one-goal lead to eventually lose on penalties but it was the celebrations of the Brentford fans which really got the goat of Moyes who blasted the behaviour of the Griffin Park faithful.
"I thought it was terrible. I saw a fan throw a bottle into our supporters. I said to him 'I saw your face. I saw who you were'," he said.
"He got a bottle and went right up and threw it right into the middle of our supporters."
And Moyes disagreed with the decision to hold the penalty shoot-out 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 added.
"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.
"I didn't grab him. I wanted to but obviously that would have brought more attention to the situation."