The Gunners ace broke his silence after Arsenal rejected a second and final 40million (£33m) bid from the Spanish giants on Thursday, leaving Fabregas at the Emirates for at least another season.
Spain's 23-year-old World Cup winner told The Sun: "I would be lying if I said that joining a club like Barcelona was not an attractive move for me.
"Let's be honest, there are not many players in the world who would not want to play for Barcelona."
Fabregas says the chance to play at the Nou Camp was too good to ignore after seven frustrating years with Arsenal.
He added "I'm an ambitious person and I have only won one trophy in my seven years at Arsenal - and that was the FA Cup.
"That's not a good enough return. We must now try and put that right. But Arsenal have made it clear they do not want to sell me.
"That's their prerogative and there's nothing I can do about that.
"I will respect it and now focus on Arsenal."