LMA chief executive Richard Bevan said there had been "aggressive and seriously undermining communications" that had made McLeish's position untenable.
Bevan said: "Alex decided he had to resign as there had been serious issues for some time between him and the board at Birmingham."
He added: "The LMA recognise it is often very difficult for clubs and chairmen, especially with the financial pressures and 24/7 media coverage. However, it is very disappointing that some clubs don't follow normal principles of employment law - which can undermine the game, the club and even the community the club is based in.
Blues' acting chairman Peter Pannu has said he will seek compensation if McLeish moves to Aston Villa.
"Mr Pannu, a senior member of the board, has put into the public domain confidential information contained in Alex's contract," Bevan added. "This is without doubt a breach of confidence.
"It is disappointing that Alex appears to have been criticised for sending his formal resignation letter by e-mail, particularly given that one of the issues Alex resigned over was Mr Pannu's sacking of Alex's chief scout, who learned that he was to be dismissed when he was copied in on an e-mail from Mr Pannu to one of the club's officials.
"There were other issues as well, including not being properly consulted on player transfers, and making a number of aggressive and seriously undermining communications, which ultimately made his position untenable."
Paul Montgomery was sacked as Blues' chief scout last month after just over two years in the job.
Pannu has said that McLeish can leave the club "with his blessing", telling Sky Sports: "I have nothing against Alex McLeish. If he moves to another place, he will go with my blessing. But it will be done properly as per the contract."
Source: PA
Source: PA