Stoke claimed a 1-0 victory at Goodison Park after referee Lee Mason adjudged James McCarthy to have fouled Bojan int he 38th minute, and the Spanish forward slotted in the resulting spot-kick.
But Martinez felt there was no contact between the players and that the penalty should not have been given.
He told Sports: ???Players from other countries ??? and I know that culture very well ??? you get brought up trying to force the ref to make a decision.
???There???s no contact with the feet, both jump off the ground which is always a sign of trying to get a decision, there is minimal contact between the arms or upper body. For me, it???s not a penalty.
???That was 45 seconds that took the game away from us.???
The referee felt James McCarthy had fouled the former Barcelona player, just moments after he only awarded a yellow to Jonathan Walters after he brought down Leighton Baines as the defender headed towards goal.
And Martinez could not understand why the Stoke player was not dismissed for denying a goalscoring opportuinity.
He added: ???For me, there is no debate. The referee sees the infringement and gives the free-kick and awards a yellow card. I don???t understand that. The free-kick is an assessment of whether it???s a good position to score a goal, whether it???s a goalscoring opportunity or not.
???Clearly Leighton Baines is running towards a one-on-one with Asmir Begovic in the central area, not from the wide areas.
???If there is a free-kick, then there is a red card.???
There were murmurs of unrest in the crowd as his Everton side left the pitch at full-time, but the former Wigan boss was more concerned with the officials.
He added: ???Stoke came with a clear attitude of a very good defensive intensity and they got a goal out of it and from that point on it became very difficult. Though I believe we created enough chances in that first half to at least get a goal and it would???ve been a completely different second half from that part of view.
???They ??? Bojan and McCarthy – are fighting for the ball, and that is nothing. It is the minimal contact and it???s what happens in football.
???It is very disappointing, and it???s not enough contact to get a penalty. It comes on the back of a very important moment because there is a difference between playing against 10, than 11 men.
???The laws are quite clear and it shouldn???t make a difference who ??? whether a striker or a defender – was in that position. The law says it is a goalscoring opportunity and Baines gets ahead of Walters so it is a clear goalscoring opportunity in my mind. I don???t get the yellow card punishment.???