Costa was on target twice as Chelsea prevailed in a thrilling encounter at Goodison Park, taking his personal tally to four in three Premier League games following a high-profile move from Atletico Madrid.
However, his on-field behaviour infuriated Everton manager Martinez, who felt Costa was guilty of taunting Seamus Coleman after the defender's second half own goal.
"I think there are certain foreign players who, when they come to the Premier League, they need to understand the ethics," said a frustrated Martinez.
"It is a completely different culture and the last thing you want to be is disrespectful from a player to another player, even if he is on the opposing team.
"I am sure he will learn that very quickly. The last thing I would do myself is fall into a trap and be disrespectful that way."
Everton goalkeeper Tim Howard was booked after rushing out of his goal to confront Costa following the forward's apparent comments towards Coleman.
Martinez added: "There is a real respect in the league and you can understand why the players weren't happy with that, the same way he [Costa] was trying to win free-kicks with the way he was playing.
"It is going to take a little bit of time to understand this league is quite different and unique and it needs players to adapt to it rather than the league adapting to them."
Chelsea boss Jose Mourinho felt his player had been the victim of provocation from Everton.
"The only thing I didn't like from this game, apart from our defending, was that some Everton players were trying to create problems for Diego," said Mourinho.
"I don't think this is English football. It's also a contradiction for Everton because everything they normally do is good and positive. To be chasing yellow cards for a player of good behaviour, that is disappointing.
"Diego is maybe the best player in the Premier League in the first three matches but he now has two yellow cards. One against Burnley when he didn't simulate and it was a clear penalty, and today everybody was chasing cards to try to get him in trouble."
