Francesco Molinari said he felt a sense of disbelief after becoming the first Italian to win the Claret Jug, adding that the fact he achieved it while playing with Tiger Woods – who held the outright lead at seven under at one point – made it even more special.

“Tiger himself was great today,” said Molinari, who joked that he might make the headlines back in Italy given Ferrari did not win the German Grand Prix. “He showed really good sportsmanship with me. Obviously, there’s a lot more people [around] if you’re grouped with him than if I’m playing some of the other guys.

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“I’ve played with him before in Ryder Cups and in big occasions, so I knew what was coming, and I was ready for it. I was calm – you know, as calm as you can be playing in the last round of a major close to the lead, playing with Tiger. I focused on my process and on hitting good shots and on playing smart golf.”

The 35-year-old from Turin, who was inspired to become a golfer after watching Costantino Rocca on TV going close at the 1995 Open at St Andrews, said he hoped his win would have an inspirational effect on others back home. “The last round already was big news in Italy. Obviously, to achieve something like this is on another level. Hopefully, there were a lot of young kids watching on TV today, like I was watching Costantino coming so close. Hopefully they will get as inspired as I was at the time, watching him vie for the Claret Jug.

“To look at the names on that Claret Jug, obviously, what can you say? It’s the best golfers in history and to be on there it’s incredible. From someone like me coming from Italy, not really a major golfing country, it’s been an incredible journey.”

Molinari, who won with a total of eight under par, also said he was proud of his feat of managing to stay bogey free through the weekend, when the wind became more of a factor for what was his third win of the season and his first major title.

“For the first time I felt I was ready for it. Winning at Wentworth and in the States,” said the Italian, whose triumph at Carnoustie forced him to cancel plans to leave Scotland on a 9pm Easyjet flight on Sunday. “Not many Europeans have managed to achieve that.

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“I got here only Monday lunchtime from the States and walked a few holes, and I saw it was firm and fast and the rough wasn’t too bad,” added Molinari, whose previous best finish was tied for ninth in 2013. “It reminded me of Muirfield. Obviously, that was a great experience to play with [the eventual winner] Phil [Mickelson] in the last round and to see someone doing the job, getting the job done on Sunday. So I liked the way the course was playing but, again, it’s a beast of a course. So I don’t think anyone feels too confident when they stand on that first tee at Carnoustie.”

Molinari also admitted he tends not to contest the Dunhill Links Championship in the autumn as he has been “beaten up” on the links at Carnoustie a few times. “I didn’t particularly enjoy that feeling. It’s a really tough course. You can try and play smart golf, but some shots you just have to hit it straight. There’s no way around it. You can’t really hide.”

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He added that he only started to believe he could win it when the young American Xander Schauffele missed a par putt at the 17th to slip two behind the lead with one hole to go. “I thought there was maybe a 5% chance. I couldn’t watch Xander play the last two holes, to be honest,” he said. “That’s why I went to the putting green because I probably would have felt sick watching on TV.”

Reflecting on his final score of six under par, which gave him a share of second place, Rory McIlroy said: “I don’t leave here with regrets, I played a good tournament but this week is just wasn’t good enough.”