The Everton boss called out the 25-year-old for appearing to goad Seamus Coleman after the Irishman's own goal and attempting to buy cheap free kicks.
Costa scored twice as Jose Mourinho's men ran out 6-3 winners over Everton after a frantic encounter at Goodison Park, and has now netted four times in his first three games in a Blue shirt.
But the Brazil-born Spaniard was also at the center of controversy, being booked for an altercation with Seamus Coleman before riling Tim Howard by appearing to goad the Irishman in the seconds after his own goal put Chelsea 3-1 ahead.
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After the match Mourinho suggested the Everton players had tried to get Costa sent off, but Martinez believes the 25-year-old has a lot to learn about the culture of the English game.
"I think there are certain foreign players who, when they come to the Premier League, need to understand the ethics and it's a completely different culture," Martinez told reporters. "The last thing you want to be is disrespectful to another player even if it's in the opposing team. I'm sure he'll learn that very quickly.
"The behavior on the pitch is quite unique in the British game. There is a real professionalism in the league and a real respect.
"You can understand why the players weren't happy with [Costa's apparent goading of Coleman], in the same way he was trying to buy free kicks with the way he was playing.
"I think it's going to take a bit a time for him to understand that this league is quite different, quite unique and it needs players to adapt to it rather than the league to adapt to the players."