The club's Russian billionaire owner Roman Abramovich has gone through seven managers since buying the club in 2003, a revolving door policy that has cost around 100 million pounds in compensation, salaries and pay-offs.
The situation led one of those seven, Brazilian World Cup-winning coach Luiz Felipe Scolari, to describe the job as "hell" for the next incumbent of the hot seat.
"Looking for what is an eighth manager in nine years is a serious embarrassment to the owner, the club, the fans and the league," LMA chief executive Richard Bevan said in a BBC Radio interview on Monday.
He said Abramovich's notorious lack of patience had undermined Villas-Boas and could be a problem for whoever is hired to replace the Portuguese.
"Players need to know that the manager's strategy and his job is not in question, there's a clear remit," Bevan said.
"You get success if you get time, and stability will come from that. Otherwise it's very difficult for a manager like Andre to impose his philosophy and build a team."
Villas-Boas attracted sympathy from fellow managers.
Arsenal manager Arsene Wenger said the 34-year-old was not given enough time.
"All I can say is I feel sorry for Villas-Boas because I know him and I like him as a manager and as a man," Wenger told Arsenal's website.
"I feel sorry for him and it's sad every time a manager loses his job because it's a job that demands a full commitment and I think he did that. I am sorry he was not given enough time to do his job."
Business analysts also suggested Abramovich's spending power made the Chelsea manager's job particularly precarious.
"Having the unrivalled spending power that can be provided by Abramovich can be a real burden," said Professor Cliff Oswick, head of faculty management at Cass Business School.
"For other managers, who don't have so many superstars or the unlimited spending power available to Abramovich, the focus is on managing with the limited resources at hand.
"In the latter situation the managerial emphasis is upon morale, motivation and development rather than acquisitions. In short, Villas-Boas may have done better with fewer resources."
Chelsea have left former player Roberto Di Matteo in temporary charge while Eddie Newton, another former player, will join the coaching staff until the end of the season.
