The former Barcelona midfielder insists that he will not be affected by any backlash at the Emirates Stadium to his decision to join their Premier League rivals
The Spain midfielder spent eight years with the Gunners and was named their captain before leaving to return to Barcelona in 2011.
Arsenal retained a first option on the 27-year-old if the Catalan side did decide to sell but opted not to exercise it before he agreed to join their London rivals.
"I'm mature enough for that [reaction] not to hurt," Fabregas told the press. "I have explained it well. I've always been very loyal and grateful to Arsenal.
"There was a first option they could exercise - I talked with Arsene Wenger and he told me that the area was covered with Mesut Ozil - but there is always fans who want to cause trouble."
Fabregas has also revealed that he asked to leave Barcelona after three mixed seasons in La Liga. He played under three different managers but only won the Spanish title once.
"There was a certain point when I took the decision and spoke to Andoni Zubizarreta [director of football] and the president [Josep Maria Bartomeu] and asked them to help me make the best decision," Fabregas explained to Cope.
"There were many, many factors. My numbers weren't bad but it's true that in big games I didn't manage to find those goals or assists.
"But I leave satisfied. I have played with my friends and experienced incredible moments in Camp Nou and outside. For me it was a great period but it's over and I wanted to find something new. I asked to leave."