Having followed in his father Angelo's footsteps by helping FC Internazionale Milano to Europe's top title, president Massimo Moratti said he was glad his family "had been good for Inter".

Saturday's 2-0 victory over FC Bayern München in Madrid completed the treble for the Serie A and Coppa Italia winners, who were contesting their first European Champion Clubs' Cup final in 38 years. They had not landed the continental crown since back-to-back triumphs in 1964 and 1965, when Angelo Moratti oversaw coach Helenio Herrera's work. Reviving the 'Grande Inter' subsequently became a driving ambition for Massimo Moratti.

After 15 sometimes difficult years in charge, he welcomed his finest hour with the joy of a child, yet insisted his achievement would not eclipse his father's. "There's just one 'presidentissimo' and that's my father," said Moratti Jr, who aged 20 had watched Inter beat SL Benfica in the 1965 final at San Siro. "I feel the responsibility of being his son, but his team will always be like the Beatles – peerless."

Touched by the supporters' celebrations, Moratti also expressed his gratitude to José Mourinho for having helped fulfil the dream. The coach's future may lie elsewhere, but if so the parting gift could hardly be more precious. "He is a great trainer," Moratti said of the man with whom he has established a strong rapport since his appointment two years ago.

"He works hard, is intelligent and sometimes surprises people with his ideas. He is a communicator, a motivator. It's not easy to find someone with all these qualities. We won this trophy because we have someone like him among us."

Moratti inherited not only an oil company from his father, but also a huge love for and commitment to Inter, which is why he wanted the generation of 1965 to be part of the Nerazzurri contingent in Madrid. "My father taught me an idea can become reality," the Inter president is fond of saying.

Sandro Mazzola played in both Inter's previous European Cup successes, scoring twice in the 1964 win against Real Madrid CF. He sees many similarities between the two sides the Morattis have built.

"The Grande Inter were a team that knew how to score goals with three passes," said Mazzola, invited by Moratti to the final along with his former team-mates. "That's what happened on Saturday when Diego Milito scored the first goal. That was the fruit of hard work, the hard work that the coach had in mind and managed to transmit to his players."

Besides Mourinho and Moratti, a third M had a massive part in Inter securing the first triple crown in Italian football history – 30-goal striker Milito scored in the Coppa Italia final and in the Scudetto-clinching victory at AC Siena, in addition to netting twice in the UEFA Champions League decider.

"I knew Diego was a goalscorer, but he is much better than I thought," said Moratti, 65. "He is a fantastic player who scores a lot, but he's also a fantastic boy. From a human perspective he is great for the squad. I just want to give him a hug because Diego is fantastic. I would like to thank him very much."

Captain Javier Zanetti, who joined Inter in the year Moratti Jr became president, 1995, also commands special attention. At 36, the Argentinian international remains an example to his colleagues, so much so that Mourinho believes his passport must have the wrong date on it.

"The final was his 700th game for Inter," said Moratti. "He was the first player I signed. He was my personal choice because I saw him playing for the Argentina Under-21s when no one else in Italy knew him. The newspapers asked: 'Who is this Zanetti?' But now he could win the Ballon d'Or for his career. He has been a fantastic player."

If no specific awards exist for club presidents, Moratti is not complaining. The respect of Inter's fans, together with the colour photo of him lifting the European Cup that will be placed at Inter's training base alongside a black-and-white equivalent of his father, is reward enough.

"For so many years he has dreamed of this – to have the same photo his father had with the European Cup – and I am very, very happy to give him it," Mourinho said.