Martinez accepted his team were poor in the first half and that only goalkeeper Ali Al Habsi played to standard, but he believes Fabregas helped ensure Arsenal took all three points.
"I know Cesc very well. He is a wonderful player and very clever, and he knows how to buy decisions off referees," he said. "There is contact, but you do not know how much of that comes from Cesc looking for it or from Gary's leg. I don't think that contact is intentional to bring Cesc down.
"Cesc comes from different culture - you do not cheat. If you take a decision from the referee it is because you are clever and you are getting something for your team.
"In England, to do that is cheating, but in South America, Spain, even Italy, to try to get a decision from the referee is just being clever and getting that advantage. Everyone is allowed to do it.
"That action in Spain gets a 'well done' from everyone. In England, they won't be too happy with because it is a completely different approach to the game."
While Martinez was disappointed with the first-half showing, he felt they improved after the break.
"I was extremely pleased with the reaction in the second half, and we frustrated Arsenal until the red card, when obviously the game it taken away from us," he said.
"Today is a painful lesson, but we take it and learn from it if we are going to come here and win against a team of the magnitude of Arsenal."
Arsene Wenger, meanwhile, felt Arsenal delivered an "outstanding" and maintained there was still more to come.
"It was a good team performance overall," he said. "The players were a bit frustrated at half-time as they did not take their chances, but during that first half, we played outstanding football.
"We feel stronger and stronger in every single game. It is interesting the chance we have in front of us because for me the way we play is fantastic to watch. Let's just keep going."
Wenger said he did not want to risk over-using Van Persie, who missed much of the start of the season through injury.
"It is down to us to use him in the right proportion of the games we play," he said. "Robin handles it all right. He is intelligent but of course he wants to play.
"We will rotate - we have no choice. We play nine games in January, it's the most we have ever played, but we have fantastic players on the bench and it is very important because we cannot always play with the same XI."
Arsenal are short on cover at the centre of defence, but Wenger maintains he will not be forced into a panic buy during January.
"I am open-minded on it and if the right opportunity turns up we will take it," he said. "It is not just because you want to buy that you find exactly what you need.
"Trust us, if the opportunity is there, we will take it; if it's not, we will play with the players we have, and I will not use that as an excuse if we don't win trophies."