The Italian stable had a dismal 2011 campaign by their lofty standards, claiming just one race victory at the British GP.
Lacking the pace needed to challenge the Red Bulls, Ferrari also fell behind the McLarens, finishing third in the Constructors' Championship.
Di Montezemolo, though, is adamant his team can turn their fortunes around next season.
"Work is going on in all areas to improve: from the design of the new car, to the simulation work, from preparing for the pit stops, to the starts and so on," he said.
"We cannot be happy with the way this year went and there is a great desire to redeem ourselves, because results don't come on their own, they are not delivered by a stork.
"It will take hard work from every one of you, it will come from the ability to be perfect, to start from pole position and that ability is the strength of this company. Behind amazing products there are amazing men and women."
He added: "All the ingredients are in place to start winning again."
The 64-year-old, who was speaking at Ferrari's Christmas lunch, which was attended by all the men and women who work on the racing side for the Maranello company, also fired a warning shot at one of his own drivers, Felipe Massa.
The Brazilian was disappointing this season as he failed to reach the podium and instead only made headlines through his on-track battles with Lewis Hamilton.
And his President has warned him that he needs to up his game next year, which could be his last with Ferrari.
"Great things are also expected from our drivers for next season," di Montezemolo said.
"Felipe knows next year is very important for him, but it is up to us to give him a competitive car. If we manage it, then I am sure we will rediscover the Felipe who delivered so much and who could be quicker than Michael and Kimi.
"Fernando has had an amazing season, even though he did not have a competitive car and he made us all happy at Silverstone, with an emblematic victory, given it came at the same circuit and in the same month in which, sixty years ago, Ferrari took its first ever Formula 1 win.
"What I like about our drivers is their ability to work with the team: I knew that about Felipe and it was a pleasant surprise to find out the same applied to Fernando.
"I don't like drivers who turn up at the track with their briefcase and do not share in the daily life of the team: they are not Ferrari people."