The former Arsenal midfielder is confident that La Roja's dominance is not over yet, and hailed the "really nice" atmosphere within the team
La Roja defeated Italy in the Euro 2012 final on Sunday to become the first team to secure back-to-back Euro titles, and the first to win three consecutive international tournaments.
As Spain switch their focus to the World Cup 2014 qualifiers, Fabregas hailed the insatiable hunger of his team-mates.
"Everyone thought we would be finished after the World Cup because we had won the Euros and the World Cup," he told The Telegraph.
"They thought we might ease off a bit but here we are again, at the European Championship again as winners, and we did the treble. Nobody has done that before in football and we are very proud of it.
"We are mostly between 23 and 25. It is really something to perform at the top level at that age.
"We were lucky to have a lot of good experiences when we were at the young age of 21. Hopefully that and the success we are having now will mean we are stronger for those experiences when we are 27 and 29.
"The age says that we can keep going for many years but, at the same time, we will see how we arrive in Brazil [for the 2014 World Cup]."
Jordi Alba played a leading role for the European champions, and Fabregas is hopeful that the 23-year-old's example will inspire young players like Thiago Alcantara and Iker Muniain to battle for a place in the squad.
"They have to keep going," Fabregas said of the new generation. "Xavi, Iker Casillas and Carles Puyol have been going for 12 years.
"They have to keep going, they have to take more responsibility. Take Jordi Alba, he played an amazing tournament, played an amazing game in the final and he is only 23 years old."
Questioned about the formula behind Spain's success, Fabregas told The Sun: "This group is more than just a team. We are friends. We like to play cards, to be together. It is something else.
"It is not a football team - it is more than that. "It is difficult to say how we retain the hunger.
"We are just so normal, we are normal people. We hang out, we play table tennis.
"We go to the cinema together, all the families are together when they come to tournaments. It is a really, really nice atmosphere."