Rocca was the country’s most successful player, and went close to winning the Claret Jug in 1995, losing a play-off to John Daly at St Andrews having famously holed a 60ft birdie putt on the 18th to tie the American.
Rocca also beat Tiger Woods in the 1997 Ryder Cup at Valderrama and Molinari coincidentally played alongside Woods in the final round at Carnoustie, where a flawless closing 69 saw him become the first Italian winner of a major title.
“It feels weird,” said Molinari, who has now recorded three wins and two runners-up finishes in his last six events.
“Costantino still is and will always be my hero and my idol.
“His text [Sunday night] was probably one of the most special ones. He came so close to winning this that it’s for him as well.
“He told me congratulations and how pleased he was for me. He knows how hard I’ve been working to get here, so I think he felt the same proudness that I felt.”
Molinari revealed that the treasured Claret Jug had spent the night on his bedside table although he did not get much sleep as he celebrated his triumph.
“It wasn’t too wild, there was a lot of joy from everyone, but a lot of tiredness as well after a long week,” he said.
“But it was great to have a few close friends and my wife having a few drinks and telling a few stories about the week.
“It’s not a nice feeling when I don’t see the Claret Jug. I want to know where it is, so I try to hold on to it as long as possible.
“Looking at the list of names on the trophy, the people who won here in Carnoustie, it’s just an incredible achievement, especially when I think where I started in Italy, not really tons of golfers there, so to come all the way to this really means a lot.”
Ryder Cup captain Thomas Bjorn believes Molinari has the ability to win multiple major titles, perhaps starting with next month’s US PGA Championship.
Molinari enjoyed bogey-free rounds of 65 and 69 at the weekend to hold off challenges from the likes of Woods, Rory McIlroy and Justin Rose.
Molinari’s spate of wins means he has secured a third Ryder Cup appearance in September and climbs to a career-high of sixth in the world.
“He’s achieved in two months probably what most European golfers want to achieve in a career,” Bjorn said.
“He won the BMW PGA, he won in America and then the Claret Jug. It’s pretty special. I was impressed with the way he went about his business.”
Asked if Molinari could win more majors, Bjorn added: “He certainly has that type of game where he can go out and challenge the best players in the world.
“He’s a different character. He just goes about his business, does it quietly, easily, but the way he played on the weekend with no bogeys, I think that’s probably the thing that would impress most players within the game. That doesn’t happen very often, especially around that golf course.
“This was a special moment for Francesco, but it was a special moment for European golf because this was for one of the hard workers and good guys of the Tour.
“He’s got another major championship coming up and with the form he’s in this could turn into one of those very, very special years.”
Molinari joked at the presentation ceremony about the size of his coaching team, but has fully reaped the rewards of working with putting coach Phil Kenyon and performance coach Dave Alred, who is most famous for his work with England rugby and World Cup-winning kicker Jonny Wilkinson.
“I’ve never won too much in my career until the last month or so and then everything seemed to be happening at the same time,” Molinari said. “It’s going to take time to really sink in.
“I know I won, but for me to realise exactly what I’ve done and what this means for me and Italian golf – and also for the remaining part of my career – it will take some time and hopefully I can take it as motivation to work even harder and try to achieve even greater things. It’s been a long, long journey, a lot of tough moments, a lot of good moments, but this beats everything by far.”
Rocca said: “I was very emotional, maybe more emotional than him. He played so good all week.
“He improved a lot the last two years and I always say if I’m still the best player in Italy after 20 years I don’t do a very good job. Now I can say I do a very good job.”