The 35-year-old London-based player spoke about the thrill of coming out on top against playing partner Woods in the final round after waking up to the sight of the Claret Jug at the side of his bed and realising Sunday hadn’t been a dream.
Woods, bidding for a 15th major title but first since 2008, was out in front on his own with eight holes to play but ended up joint-sixth, three shots behind, after Molinari closed with a bogey-free 69.
“Tiger was really great to play with, and when he took over as the sole leader, I told myself I mustn’t start watching what he was doing – just focus on my game, and what I needed to do to catch him.
“As much as possible I tried to treat him like any other player, and not be too impressed by what he was doing,” said Molinari.
“But now it’s over, I can admit it makes it even more special that I was playing alongside Tiger when I won The Open, and that he was like the old Tiger, fighting hard for the trophy and playing unbelievable golf.
“He was obviously the best player on the course over the front nine, and you could feel the excitement growing.
“Then he hit a couple of loose shots, unfortunately, and you will always pay a heavy penalty on a course as tough as Carnoustie.
“But he was very generous in congratulating me, and I think we can all see that he is back as a strong force in these events.”
Molinari’s historic win meant him staying in Carnoustie for an extra night after missing an easyJet flight he was due to be on from Edinburgh to Gatwick at 9pm on Sunday.
“Waking up with the Claret Jug on my bedside table was amazing, incredible,” he admitted. “It’s been a long night, not much sleep – about three hours – after a good night of celebrations.
“It wasn’t too wild. There was a lot of joy, but a lot of tiredness too. It was just me, my wife, my caddie, my agent and some friends having a few drinks and telling stories about the week.
“I’m not a big drinker, so there won’t be many tales of alcohol being drunk out of the Claret Jug. But it was nice to stay up late toasting it with champagne and clinking the glasses against the spot where my name is engraved.
“I didn’t want to go to bed – I just wanted to stay awake as long as possible, looking at the trophy, to make sure it had really happened. It’s not a nice feeling when you let it out of your sight.
“And you are afraid you will wake up and it was all a dream. But, thankfully, it was still there when I woke up.
“I cannot wait to get back to London to show the Claret Jug to my children, and see if they realise just how much this means.
“If they don’t realise it, I will find a way to let them know how big it is. And I have to take it back to Italy as soon as possible to show it to the rest of my family. They are a big part of all I do.”