A social media feed dedicated to tracking the fortunes of Scottie Scheffler posed a question to its followers on the eve of the Open’s final round: ‘What would Rory have to shoot tomorrow to win?’ The most popular response was succinct: ‘Scottie.’

In truth, Rory McIlroy would have needed to find a way to outmaneuver not only Scottie Scheffler but also Harris English, Wyndham Clark, Haotong Li, Chris Gotterup, and Matt Fitzpatrick to have any chance of securing victory at Royal Portrush.

Sunday became a day to admire the unyielding brilliance of Scheffler but equally a day of disappointment for the masses of McIlroy supporters who flooded the Dunluce Links course with the hopeful expectation of watching their local hero close the six-shot gap that world No 1 held at the start of the day.

The incredible energy that had mobilised behind McIlroy and rolled around this spectacular course on Saturday, filling him with brilliance and momentum on his way to a round of 66, was never quite replicated on the final day.

From the moment McIlroy left a birdie putt short on the first green, his round never accelerated. By the time he got to the second green, the digital screen by the side of it showed that Scheffler had birdied the first. McIlroy was now seven shots behind the leader.

McIlroy did birdie the second but it could not disguise the gulf between him and Scheffler. The American is not the type to succumb to a meltdown. The idea that there could yet be a six-shot swing to hand McIlroy the advantage felt fanciful in the extreme.

The fans willed McIlroy on, of course. As he walked between the first green and the second tee, they yelled encouragement. When he high-fived a kid next to the ropes, the lad turned to his dad and pumped his fists in delight.

But by the fourth, as it became clear that Scheffler was going to be rock-steady, McIlroy’s shoulders had slumped a little. He sliced his second shot on that hole and glared after it as it flew towards the green, before swishing his club in frustration and yelling out a warning of ‘right’.

His ball came to rest in thick grass at the edge of the green above the hole. It left him with a shot to nothing and all he could do was chip it out and watch it roll down the hill to leave him with a 30ft putt for par. He didn’t make it.

On the fifth, he boomed a drive into undergrowth on a bank to the right of the par four. He had to leap up and down from where his ball lay to see where the flag was. His head kept appearing and disappearing, appearing and disappearing.

Behind him, the digital screen showed he was now eight shots adrift of Scheffler.

It is a mark of McIlroy’s genius for recovery that he still made birdie on the fifth. That brought a roar from the crowd but a couple of minutes later, Scheffler’s ball thudded into the heart of the green and came to rest 10 feet from the hole. The crowd groaned in disappointment.

Scheffler has been on a different level here in Portrush. A different level to McIlroy. A different level to everyone. He only needs to win the US Open to complete his own career Grand Slam, the ambition McIlroy fulfilled when he won the Masters in April.

McIlroy and Scheffler are the two greatest players of the post-Tiger Woods generation and the contrast in their styles and their demeanours makes their rivalry all the more compelling. McIlroy’s brilliance is wild and unpredictable and charismatic, Scheffler’s is controlled, consistent, metronomic and reserved.

Part of what makes McIlroy’s golf so breathtaking is his ability to recover from apparently lost causes. Part of what makes Scheffler’s golf so breathtaking is that he very rarely flirts with lost causes in the first place. The commanding nature of Scheffler’s win here will establish him in many minds as the heir to Woods but it is only a few months ago that McIlroy was winning one of the most dramatic tournaments in golf history at Augusta National to seal his fifth major.

Scheffler, though, has time on his side. He is 29, seven years McIlroy’s junior.

It has still been a stunning year for McIlroy but it is as if the emotional effort he expended to win a Green Jacket at last has drained him of the requisite strength and singularity of purpose to rise to a similar peak since.

By the time McIlroy birdied the 15th to move to 10-under, he could only manage a weary wave to the galleries. Scheffler was still seven shots ahead. When he dragged his tee shot on the 16th on to the slope that plunges steeply down from the green, he threw his tee peg away in disgust. He started the day six shots adrift of Scheffler and finished it seven shots adrift of him, in a tie for seventh.

Many believe Scheffler is about to eclipse him. Even McIlroy seems to think Scheffler may be about to eclipse him. He spoke afterwards about how his wins at the start of this year, including the Masters, came when ‘Scottie wasn’t quite on his game’. He sounded defeated by Scheffler’s relentlessness.

‘All you can do is admire what he does and how he does it,’ McIlroy said. ‘What he does is one thing, but how he does it is another. He just goes about his business, doesn’t do anything overly flamboyant, but he’s the best at executing in the game right now. All you can do is tip your cap and watch in admiration.’

If McIlroy needs fresh motivation after completing his career Grand Slam, the looming Ryder Cup will provide one source of inspiration.

The battle to stay with Scheffler, to compete with him and to re-establish himself as the world No 1, will provide another.