Moyes said after Everton's 2-1 defeat that Fabregas should have been sent off for his "disgusting" comments towards the officials at half-time, although he then refused to elaborate on the content of the player's remarks.
Arsene Wenger hit out at Moyes for making comments from the tunnel public, saying he felt there was a witch-hunt against Fabregas and that the Everton manager had broken an "unwritten rule" by revealing what he "claims to have heard".
However, Moyes said: "I know what was said. I was there when it was said and we heard it. I think Arsene said there was an unwritten rule that you don't say things that are in the tunnel, but their player broke the unwritten rule. He questioned Everton Football Club, that we may be paying officials. By doing that he questioned the officials and that they may be in turn taking money.
"What I've got to say is Cesc never swore once. He was very calm and calculated - it wasn't a rant or a rave like I have heard people say it was. It was just straight to the point and I felt it was out of order and deserved a sending off.
"There is no way do I want Cesc Fabregas or Arsenal done by the FA, not at all. If the FA come asking, I will say I am not interested. If Cesc had got sent off at half-time, it would have given us a better chance of winning the game, but the game is gone now.
"But to question Everton's integrity, to question David Moyes' integrity and to actually say that you think David Moyes did not see it or hear it ... I saw it, I heard it. I was standing there. It was aimed at the fourth official. The fourth official is part of the referee team.
"If I had shouted at the fourth official on the side of the pitch, if I had swore - which I have done and I am not proud of ... I have shouted at them, but I would not have said what he said."
Wenger insisted Fabregas "did not say anything to the referee", but Moyes said: "Arsene seems to think that I haven't seen or heard it, but you have to decide who you believe - David Moyes or Arsene Wenger - and I'm happy for people to make their own mind up on that."