The Stamford Bridge club have had eight managers in nine years since the Russian billionaire took over at Chelsea - with Andre Villas-Boas sacked after just eight months.
The club were labelled a "serious embarrassment" by the LMA after the Portuguese's sacking and now LMA chairman Howard Wilkinson has turned his fire on Abramovich himself.
Wilkinson told journalists: "Clearly, it seems to me that Roman Abramovich is not aware of the difference between having a successful team and building a successful club.
"The evidence shows that the successful clubs - ones that have been constructed in a planned, long-term and strategic way and which have a vision of where they want to go and know how they want to get there.
"What happens is that the product of that is they continue to produce successful teams. The lesson is that if you want to be winning things then history shows that is the way that you have got to go.
"To see that you just have to look at two clubs at the moment - Manchester United, who have been the most successful club in England over the last 15 years, and Barcelona who have also enjoyed sustained success."
Wilkinson suggested Jose Mourinho's departure in 2007 may have been because Chelsea were not looking long-term.
He said: "Certainly managers who have the capacity to look long-term such as Sir Alex Ferguson and Pep Guardiola and also Arsene Wenger also have an enormous amount to contribute to the development of a successful club.
"I don't know Jose Mourinho inside-out but from the outside looking in it would seem that he had that capacity but clearly that wasn't part of the deal at Chelsea and that is why he left."
Wilkinson added Manchester City had appeared to be taking the right tack.
He said: "There seems to be a conviction at Manchester City that the club grows and stands for something and that the club then becomes bigger than any individuals within it and individuals have to go along with the direction that the club has decided it is going to travel along.
"Somebody once said that copying successfully is genius. Everybody is looking to learn and if you can learn from your neighbours who have been there, seen it, done it, well you would be a fool not to follow their example."