Fabregas was seen to launch a tirade of abuse in the direction of referee Lee Mason and his assistant Stephen Child after Toffees' striker Louis Saha had taken advantage of a contentious decision to fire Everton in front from an offside position.
The 23-year-old reportedly carried on venting his spleen as the two teams headed down the tunnel at the break, allegedly accusing Everton players and the officials of taking bribes for allowing the controversial decision to stand.
But after Arsenal boss Arsene Wenger tried to play down the incident and deflect criticism away from Fabregas, Moyes has decided to give his version of events.
"Cesc [Fabregas] questioned Everton's integrity by suggesting we possibly had given money to the referee,” Moyes told the BBC.
"It’s been said that I didn’t see it or that I didn’t hear. Well, I was there and I saw it and I was there and I heard it. If I had said that, or if any other player had said that, it would have warranted a sending off.
"Cesc's actions were calculated. They were collected. And they were said in a way that if you or I said that to the fourth official, who he did direct it to, I think I would have been sent off.
"You have to decide who you believe. David Moyes or Arsene Wenger."
The FA have already decided that no further action will be taken against Fabregas, after Mason omitted details of the incident in his match report.
The latest controversy involving Fabregas comes hot on the heels of another incident involving Huddersfield Town winger Anthony Pilkington.
Pilkington accused the Spaniard of obscenities following a request to swap shirts at the end of a recent FA Cup tie at Emirates Stadium.
