Arsenal were a goal behind at the break after Louis Saha scored a goal from what both managers felt was an offside decision.
Gunners skipper Cesc Fabregas remonstrated with referee Lee Mason in the aftermath of the goal, but Moyes claimed that the Spain midfielder went on to makes "disgusting" comments as he left the field.
Both The Sun and Daily Mail quote an Everton source on Thursday claiming Fabregas accused referee Mason, of having been paid-off.
Fabregas has not been punished by The FA, as Mason made no reference to it in his match report, and the Arsenal captain claimed that it was "heat of the moment" stuff.
Wenger, though, believes the incident should never have been made public and has hit out at Moyes for going against an unwritten rule of never speaking of such incidents.
"For me, this is over and I believe it is wrong for Moyes to come out and say what he claims to have heard in the tunnel," Wenger said. "If I come out with what I have heard in the tunnel over the last ten years you would be amazed.
"I think there is a rule in our job to never come out with what is said in the heat of the moment. That usually is respected by everybody.
"I have heard amazing things in the tunnel. It has never come out and you have to understand that if you play with your friends on the pitch, you say things to your friend that in 24 hours you would not be very proud of, but it is in the heat of the moment."
Fabregas was also criticised after the 2-1 FA Cup victory over Huddersfield for refusing to swap shirts at the end of the game. Huddersfield's Anthony Pilkington wrote on Twitter: "2 lads asked him for his shirt and he told them to f*ck off!! Sick player but what a tit!"
Wenger, though, believes the recent criticism of his captain is unjust. Asked if he thought there was a witch-hunt against Fabregas, Wenger said: "Yes.
"We are long enough in the job to know that somebody picks on you for a while, and you are in the heat of the moment, but for me what is the most important is the player behaves well.
"When Cesc is on the pitch, he tries to play football - I cannot say everybody who plays against him tries to do that.
"For example, some people reproach him for not exchanging shirts with a player after the game - but I hope he will not exchange shirts with players who try to kick him for 90 minutes and them come to say, 'Please can I get your shirt?'.
"I think that is a normal and natural reaction. Overall this guy is an example on the football pitch and shows you how to play football."
He added: "People are more demanding, and Cesc has to live with that. It is not easy, but he is a very intelligent man and he will learn very quickly to cope with that.
"Cesc is 24 this year. He has played 250 games in the Premier League - at that age, it is absolutely remarkable. He has gone through a lot, difficult moments, but has always come out stronger. This guy is a fantastic leader."