Martinez said his fellow Spaniard was still adapting to the football culture in England after his move from Barcelona and that it was only a matter of time before his talent began to shine on the pitch.
"Gerard is a young man who has come into a very different game and he needs to understand the culture of the British game," the manager said, quoted by Sky Sports.
"But I love to see players who care and want to make things happen. He is an emotional player and I don't think he was disrespectful in any way.
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"When they keep hitting you with every chance they get, sometimes you are going to feel the challenge comes your way and maybe you are going to go to ground that little bit easier.
"Maybe he has to learn that, but it is difficult as a striker or an attacking player to cope with the amount of bad treatment you get from defenders.
"He is a young player and he has a lot to learn but he has the desire and that winning mentality and it's only a matter of time before he puts that talent together."
The defeat by Arsenal saw Everton slip to 11th place in the Premier League table, while the Gunners climbed to second place behind leaders Manchester City on goal difference.
(Reporting by Simon Jennings in Bengaluru)
