Gilberto feels Arsenal have the mental strength needed to mount a push for the Premiership title and also land the Carling Cup.
The Gunners have found some good form in recent weeks and they set up a Carling Cup showdown with Chelsea when getting the better of North London rivals Tottenham on Wednesday.
Gilberto is confident ahead of the Millennium Stadium final with Chelsea and also feels The Gunners are still in the title hunt, despite trailing Manchester United by 15 points.
"It was important for us," Gilberto told Sky Sports News of the win over Spurs. "I think the team showed fantastic mental strength.
"It was important for all of us.
"We can win. We know it won't be easy against a great team like Chelsea, but we have shown we can put in great performances and our last few games have been good.
"If we show the attitude we have shown, we gave a great chance."
Talk of a title charge has been played down by Gunners chief Arsene Wenger, but Gilberto has not given up hope.
"Everything is possible in football, that's why we still believe we can do it.
"I have the experience of my first season in the Premier League when we were 12 points clear of Manchester United and started to drop points, so it can be done."