Bernstein's comments about managers' touchline behaviour and criticism of officials provoked a furious response from the League Managers' Association, but Wenger 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 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."