New signing Costa taunted Seamus Coleman after the Irish defender's own goal put Chelsea 3-1 ahead at Goodison Park which prompted an angry reaction from a number of Everton players, in particular American goalkeeper Tim Howard.
"There are certain foreign players who come to the Premier League who need to understand the ethics and the culture," Everton boss Martinez told reporters.
"The behaviour in the British game is unique. The last thing you want to see is disrespect from a player to another player and I am sure he will learn that very quickly.
"There is a real professionalism and respect in the league so you can understand why the players weren't happy with that, in the same way as trying to buy free kicks with the way he plays."
Costa has been impressive in firing Chelsea to the top of the table after scoring four goals in his first three games since signing from Spanish champions Atletico Madrid in the close season.
But he has also been accused of gamesmanship. Chelsea manager Jose Mourinho thought his Brazilian-born striker was being unfairly targeted.
"To be chasing cards against a player who once more had good behaviour and was just here to play football is disappointing," the Portuguese said.
"At the end of the story, Diego is maybe the best player in the Premier League in the first three matches and he has two yellow cards - one against Burnley where he didn't simulate, it was a penalty, and one against Everton, when everyone was chasing him to get him in trouble. That is disappointing."