However, Everton's Roberto Martinez insists the criticism was a "very cheap" shot from somebody who has no experience of being a manager.
Bernstein's comments about managers' touchline behaviour and criticism of officials provoked a furious response from the League Managers' Association.
The LMA branded his comments 'misguided, unhelpful and inflammatory' before accusing the former FA chief of being uncommunicative.
"It is particularly sad to find David Bernstein celebrating his CBE by engaging in a megaphone commentary from the side-lines," said the LMA.
"Had he engaged with the LMA, his leadership would have been rather more effective and focused.
"The LMA looks forward to an engaged and constructive dialogue with the new chairman of the FA, especially as David Bernstein failed to attend a single formal managers' meeting to discuss any such issues in the game or build any kind of meaningful relationship with our members."
Wenger, however, said the ex-FA chief was right - and that he too needed to improve.
Wenger said: "I go along with that [Bernstein's comments] and I have some work to so on that front as well."
Martinez takes a different view and said Bernstein had never experienced the "unique position" of being a club manager.
The Everton boss said: "I always respect anyone who is involved in the game and has a position in the game, whichever the authority or association it is.
"But I think it is very cheap to speak about the behaviour of managers unless you have been in that position.
"It would be great for anyone to trial it and then it would be easier to understand it because of the emotions. There are many situations you have to control as a manager and sometimes they are out of your hands and it is quite frustrating to accept that."
Manchester United boss David Moyes attracted attention only this week for criticism of Howard Webb after his side's loss to Tottenham, but thinks that he and his counterparts are not culpable.
"I think managers are incredibly responsible," he said.
"The work the LMA do and what managers give back, the help they're trying to give the FA Commission, for example, I think that would be a wrong thing to say about the managers."
Like Moyes, Stoke boss Mark Hughes has recently had run-ins with officials and last weekend was sent to the stands as his side lost at Newcastle.
"I think what Richard Bevan has come out with, I just reiterate every word that he's said," the former Wales manager said. "It's difficult."
Chelsea boss Jose Mourinho accepted that there are times when managers can go too far on the touchline or with their comments.
"I think managers are the person in the game with more pressure on their shoulders. I think managers they have the most difficult job in the game, plus the referees," said the Portuguese.
"And I think if on isolated occasions managers, they lose their emotional control and they have a certain behaviour that cannot be accepted by the authorities, in this case by the refs, I think we should be punished.
"But be punished in a way where people don't feel the managers are strange or weird or impolite people, or people without control."
Manchester City's Manuel Pellegrini has by and large stayed on the right side of the law since taking over last summer.
"I think it is very difficult to be a referee. The players play too quickly, the players are always trying to cheat because football is cheating," he said.
"I think it is very difficult and I respect them (referees). Of course nobody likes it when the referee whistles against your team when it is wrong, but a lot of time he whistles and gives you an advantage that maybe you didn't have."