Reacting to the criticism of Chelsea from Arsenal fans after the 0-0 draw last weekend, with The Emirates crowd decrying them as boring, Burley felt Gooners missed the point.
He said: "Is it any wonder Cesc didn't go back to Arsenal? Why on earh would he have gone back to Arsenal to win nothing, when he could go to Chelsea.
"They're boring but theyve for the second best scoring record in the league?
"When did they last win a title? Theyv'e paid the most money (fans), they pay their cash and they win nothing.
"Arsenal have entertained, probably the best in the last 10 years. How many titles have the won?"
Chelsea boss Jose Mourinho had in response told The BBC that Arsenal were the boring ones, going 10 years without winning a Premier League title, while defender Kurt Zouma was quoted by The Sun saying Gunners fans were simply jealous of their success.
Fabregas has always maintained it was Arsenal who did not want him, quoted in The Mail last year saying the club turned down the chance to re-sign him from Barcelona.
Arsenal boss Arsene Wenger has suggested differently, telling SkySports that his former captain chose Chelsea, with the deal done months in advance.