The Scot was removed form his post on Tuesday but the LMA have derided the whole affair as "unprofessional".
Their discontent is rooted in the fact that reports that Moyes was to be dismissed had emerged 16 hours before the coach had been called into a meeting with United's executive vice-chairman Ed Woodward to be informed that his contract was being terminated. The insinuation is that United officials had leaked their intentions to the press first, although officials at Old Trafford have since denied such an accusation.
They claim instead that no official decision had been taken at the time the reports came out on Monday but that has not been enough to appease the LMA.
"The LMA is very disappointed with the nature of David's departure from Manchester United and to read extensive reports in the press, confirming David's sacking, before David himself had been spoken to officially by the club," said Bevan.
"Throughout his time at United, David, as he always does, has conducted himself with integrity and professionalism, values that he believes in and that have been strongly associated with the club and its rich tradition. It is therefore sad to see the end of David's tenure at United handled in an unprofessional manner."
The 50-year-old was castigated during the final months of his reign but Bevan is certain that Moyes will rebuild his reputation quickly. "He is passionate about the game and he possesses the drive and resilience to learn from this chapter of his career and move on to a new challenge in the game," he added.