Giulia said on Tuesday that her father Tony was one of the defining Formula 1 drivers of the 1950s.
The British won six grands prix but missed out on the world championship.
The most successful driver of his era was Brooks.
Moss is the best British driver never to win the F1 title.
Moss, who died two years ago at the age of 90, said of his former team-mate and friend: "Brooks was a tremendous driver, the greatest, if he will forgive me saying this." Several people who won the world championship were better than him.
F1 CEO Stefano Domenicali was sad to hear about the death of TonyBrooks.
He was part of a group of pioneers who pushed the boundaries at a time of great risk.
He will be missed and our thoughts are with his family.
The last surviving F1 race winner of the 1950s, and the only one who won all of his races in an era when mechanical reliability was a significant feature in the sport, was Brooks.
The Syracuse Grand Prix of 1955 was the first ever F1 race won by Brooks, who was studying dentistry at Manchester University.
After receiving a call from the team while revising, he went to Italy, missed the first practice day, learned the circuit on a Vespa, and then caused a sensation by leading home the Ferraris of world championship regulars.
His career as a dentist was put on hold as he focused on motor racing.
He entered F1 in 1956 with BRM, but he raced only twice in a car that was not a success, and was lucky to escape serious injury from a crash when its throttle stuck open during the British Grand Prix.
His breakthrough occurred the following year. After finishing second in Monaco to Fangio, who was on course for the last of his five world titles, he joined the Vanwall team and won the British Grand Prix.
Despite being injured in a crash at Le Mans, he still qualified third. Moss went on to a famous win after the fatigued Brooks handed over his car.
In the Belgian and German Grands Prix, he excelled on the most demanding circuits, and in 1958 he demonstrated his skills with victories on the Spa-Francorchamps and NurburgringNordschleife circuits.
He should have won the world title when he moved to Ferrari. He went into the final race in Florida with a chance of winning the title despite having trouble at the other races.
He did not believe in taking unnecessary risks with his life, despite his profession.
His view on how to approach his sport has changed because of the crashes. He resolved to never do that again after trying to compensate for the deficiencies in the car.
I always felt it was morally wrong to take unnecessary risks with one's life, because I believe that life is a gift from God and that suicide is morally unacceptable, he told the veteran F1 journalist in the 1980s.
I wouldn't agree with those who say that driving racing cars is unnecessary risk. While not exactly suicide, driving one which may be unsound or damaged is verging towards it.
The world title probably went to him because of the philosophy. The 1959 US Grand Prix saw a car hit a teammate on the first lap.
He said that his natural inclination was to carry on, but that he made himself come in to have the car checked over.
I lost half a lap doing that, but still finished third. Jack ran out of petrol near the end after Stirling retired. I think I did the right thing.
Although he continued in F1 after leaving Ferrari, he was already thinking of moving on. He retired after an unsatisfactory year with BRM.
One of the greatest drivers of all time, and also a charming and self-effacing man, is what the people who know motor racing will always remember.
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