The Gunners had first refusal on their former captain but ultimately declined to activate it as Fabregas ended up joining the Stamford Bridge club for £30m.
Speaking to The Sun, the 27-year-old defended his decision to sign for Arsenal's London rivals by claiming that the reception would have been hostile regardless of which English club he joined.
"Changing clubs is part of the game and people must remember it was Arsenal who didn't take up the buy-back option for me," he said. "What am I going to do - retire? No way.
"I can understand some people at Arsenal are sad, some people are upset, some people are even angry. But I have to look after myself. I had to make a decision.
"I wanted to keep playing football, enjoying myself and my career and I felt that joining Chelsea was the best option for me. There would have been a reaction wherever I had gone."
The Spaniard has enjoyed a prolific start to his Chelsea career, clocking up six assists and one goal in all competitions.