Gilberto believes Arsenal must win some silverware this season, but has warned that it will not be easy for his former side.
The Brazilian ended a six-year spell with the Gunners when he completed a move to Panathinaikos earlier in July.
Gilberto's departure followed the exits of Mathieu Flamini and Alexander Hleb, while speculation continues about the future of star striker Emmanuel Adebayor.
Arsenal have not lifted a trophy for three seasons and Gilberto fears there may be another barren campaign ahead.
The experienced midfielder has faith in the club's young players, but feels Arsene Wenger needs to be successful in at least one competition to lift pressure at Emirates Stadium.
"This is what they need to achieve - start to win things," he told Arsenal TV Online.
"Of course there is massive pressure on them, but people cannot forget they are still a young side and they have a lot to improve, to grow and to learn, but it will be very important to them if they win something this year.
"I am sure everyone at the club, Arsene, his staff, the players will do the maximum they can to achieve and win titles. This is the target and they won't change it.
"But it will be hard again. It won't be easy because the other teams are stronger than last year and Arsenal will have a hard season, but I am confident they will handle it. I hope they can win this year."
Gilberto could face Arsenal this season if Panathinaikos are drawn in their UEFA Champions League group, but he admits he would not relish such an occasion.
"I hope not, but I think, if it happens, it will be very emotional for me after leaving the club and playing against them in the first season with another club," he explained.
"It is possible. We need to consider that, but both of the teams need to qualify first. I am sure Arsenal will qualify and Panathinaikos will. We will see in the draw."