Back with the Brazil squad for their friendly in London against Italy, Gilberto said: "I never fell out with Arsene, whatever people say. I had to respect his decision even if I disagreed with it.
"We had good conversations but, when it came to talking about whether he still saw me as part of the team, it wasn't the conversation I expected. Maybe, I thought, it was time to leave Arsenal. I understood what the manager's idea was; he had so many good young players and, if I was in the team, they wouldn't have the chance to develop."
Last summer, Gilberto declined offers from other English clubs, not wanting to 'spoil the good story' of his time at Arsenal, and Panathinaikos made their move. He said: "Greece maybe wasn't an obvious choice but I wanted to refresh my mind and I'm enjoying it.
"It's good to experience a different mentality, a different culture. The club has great history and we're doing well in the Champions League.
"Even though we felt so at home in England, my family is settled and like it here."
He added: "It's only my opinion, and I could be proved wrong, but I think Arsenal made a mistake letting some of the more experienced players go. It would be good for the development of the younger players. They're having to learn for themselves and that's hard."