The 24-year-old, who has been linked with a move away from the Emirates all summer, is expected to leave for Barcelona in the coming weeks after reports have suggested that the Catalan giants will table a fresh bid for the midfielder.
While the Spain international is edging closer to a move to the Nou Camp, Robson has admitted that Arsenal will not miss him.
"You can't call [Cesc Fabregas] a leader," Robson told talkSPORT. "Thierry Henry wasn't a leader. He was, in my view, a poor captain. When things were going wrong for Arsenal he never stepped up.
"And when things were going wrong for Arsenal, Cesc Fabregas didn't always step up either. There was that game at Newcastle last year where Cesc Fabregas was brilliant in the first half and you didn't see him in the second half.
"That's where Cesc Fabregas won't be a loss as a leader because the feeling I get is that he'd lost interest in the club for a whole year and he wasn't a good influence on some of the other players."
Meanwhile, Arsenal have been preparing for their Premier League opening fixture away to Newcastle on Saturday, August 13.