The Newcastle manager was fined £100,000 and given a formal warning by his club after headbutting Hull midfielder David Meyler during his side's 4-1 win at the KC Stadium.
Pardew will face no further action from is club but is almost certain to face disciplinary proceedings from the Football Association.
LMA chief executive Bevan confirmed he had spoken to Pardew, who was "extremely sorry", and would speak to him again on Sunday.
"The buck stops with Alan," he said. "It's unacceptable, it's inappropriate and it's insupportable from every perspective and Alan knows that.
"He immediately realised the serious error, (made) sincere apologies to all parties and obviously (has) deep regret.
"It was good to see (Hull boss) Steve Bruce's reaction and Hull accepting (Pardew's apology).
"But Alan does need to think hard about how not to put himself in that position again."
"I was pleased to see Newcastle in a very short period of time making a very swift, professional response that provided Alan with a very heavy fine and a formal warning."
Bevan also confirmed the LMA was reviewing the positioning of the technical area and could move managers further away from the action.
He said: "We did a technical report six or seven months ago, interviewing 40 referees and 40 managers, and we're looking at the moment how the technical area works in America, for example, in other sports and seeing how we can look to improve several problems that occur because of the positioning."
Bevan admitted the tight confines of some grounds would pose a problem, with the manager also needing to be kept out of the fans.
He added: "But what we can do is make a serious effort to look at how the technical area should be placed."