"I'm not a (soccer) commentator," the president said, "but I thought you deserved the victory well beyond whatever happened during the penalty shootout."
Coach Mancini replied, "Let me thank you for being our No. 1 fan. We saw you exult, that gave us much pleasure."
In another compliment, Mattarella said, "You displayed a harmony of team among yourselves and in play, and now this is an extraordinary value, the sense of sport."
"This," captain Chiellini said, "is the success of a group, who even in difficult moments never lost heart.”
Mattarella also generously praised another of his palace guests, tennis player Matteo Berrettini, who reached the Wimbledon final before succumbing on Sunday to Novak Djokovic.
The tennis star, in thanks, gave Mattarella a racket, and later squeezed aboard the open-topped bus among the soccer players, who whooped and cheered themselves in response to the public's adulation.
As the bus inched its way toward central Piazza Venezia, and eventually to the team's hotel, the players, each wearing the victory medal they received less than 24 hours before at Wembley, snapped photos of the celebrating fans and encouraged them with cheers through a bullhorn.
There was enough joy to go around to even reach the 10th-floor hospital suite of Pope Francis, who, even before the Italian victory, could savor the triumph of the team from his native Argentina, which won the Copa America on Saturday.
"In sharing the joy for the victory of the Argentine national and of the Italian national squads with the persons near to him, His Holiness dwelled on the meaning of sport and its values," Vatican spokesman Matteo Bruni said in an update on the pope's convalescence in Rome following July 4 colon surgery.
Bruni said Francis spoke of "that sporting ability to know how to accept any result, even defeat."
When Premier Mario Draghi greeted each player in the courtyard of Chigi Palace, the government headquarters, he also cited the value of sports beyond playing fields and scoreboards.