The Toffees' travelling fans launched jibes at the Scotsman, who left Goodison Park to become the new boss at Old Trafford in the summer, during last night's 1-0 victory over the Red Devils.
According to Twitter user David D Wallbank, Moyes said after the game while in the Lowry hotel that the treatment he received from the fans was 'disgraceful'.
He wrote on Twitter: "Moyes 'after 11 years it's a disgrace how the fans treated me tonight. From how I found them to how I left them.....a fucking disgrace'"
It was also claimed on Twitter that the Scotsman described new Everton boss Roberto Martinez as a "great guy".
The photo of the meeting was posted on Twitter:
i have had a few beers, but I am not telling fibs on this one. He was proper angry...but was nice about Roberto pic.twitter.com/rHEVfOi2gQ— David D. Wallbank (@daveywallbank) December 4, 2013