Murphy criticised reckless tackling by some players and pointed the finger at the approach favoured by managers at three clubs - Stoke, Blackburn and Wolves.
A statement from the League Managers' Association insisted such violent tackles were not encouraged by coaches and indicated Murphy should not have spoken out, saying: "It is inappropriate for individuals to direct criticism at certain managers who are honest, professional and continue to achieve success on the field with their clubs."
The staement continued: "The accomplishments of the managers mentioned should be applauded rather than publicly judged. Professional football managers certainly do not incite their players to go out and cause injury to fellow professionals.
"Two of the three clubs mentioned have yet to receive a red card in the Barclays Premier League this season."
The LMA statement pointed out that the speed of the game and the fact players are stronger and quicker makes the impact of mistimed tackles is far greater than in the past.
Coaches instruct players not be lured into early challenges and to stay on their feet, the LMA said.
"Mistimed tackles by fractions of a second will happen and with that will be a potential risk of impact or injury but in no way does it follow that the actions are either deliberate or encouraged," added the LMA, who said managers' support staff would not back a manager who encouraged violent or reckless play in any direct or indirect way, and that if they did so it would quickly leak out.
Murphy's remarks at the Leaders in Football conference in London last week caused a storm.
Murphy said: "You get managers who are sending their teams out to stop other teams playing, which is happening more and more - the Stokes, Blackburns, Wolves. They can say it's effective and they have got to win games but the fact is the managers are sending out their players so pumped up there is inevitably going to be problems."