The League Managers' Association accused United of being "unprofessional" regarding the manner in which Moyes was sent packing.
Numerous media reports claimed on Monday evening that the Scotsman was to lose his job, but it is believed that Moyes was only told of the club's decision on the morning that he was sacked.
"It's very difficult when a huge decision at a big club is made in this day and age to keep it quiet," Moyes told reporters in Friday's press conference. "Somewhere, someone knows about that situation.
"It's very similar to the situation I found myself in when I was relieved of my duties at Manchester City. Everybody knew the morning of the day I was getting sacked.
"This week will hurt and it will hurt for quite some time I would suggest. It affects not only you but your family and people close to you. Sometimes people forget that."