Fleetwood, and the reigning European No 1, confessed his 'time was up' after posting a third round 74 for a six-under par total on day three of the DP World Tour Championship in Dubai.
It left Fleetwood trailing eight shots adrift of the Masters winning leading duo of American Patrick Reed (67) and England's Danny Willett (68).
Molinari, like Fleetwood, has also struggled this week and posted a third day 70 to be sharing 28th place at five-under par and one behind Fleetwood.
Fleetwood knew in teeing-up this week on the Earth Course in Dubai he needed to have to win the DP World Tour Championship to have any chance of denying Molinari but now that's virtually out-of-the-question as the Englishman knows.
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I think you kind of know when your time's up
"I think you kind of know when your time's up," he said.
"I lasted within two days of the season. Like I've said, it was a stretch trying to win it. But it is what it is. I'll play tomorrow and we'll see how we do, but it's fine
"At the end of the day, you live and breathe the game, don't you, so there's going to be good bits and bad bits
"Today pretty much summed up the sort of second half of the season. I've done plenty of good stuff in tournaments, and then days like today.
"But it is what it is. I'm fine. Hit and healthy. I'll play golf tomorrow and that's it. I'll go home and I'll spend time with my son tonight. At the end of the day, it's just golf, but it does hurt when you have days like that."
For Molinari becoming the European Tour No 1 is the cherry on a brilliant 2018 cake.
The modest 36-year-old became the first Italian to win a Major in capturing the Open Championship at Carnoustie.
He also became the first player in the history of European Ryder Cup competition to win all five matches last month in France.
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And the accolades will continue for Molinari such as the prestigious AGW Golfer of the Year award, the European Tour Golfer of the Year while on December 19 he will be in Rome to become the first Italian-born non-Olympian to be presented with the Collare d'Oro al Merito Sportivo medal.
"It would mean a lot, no doubt," said Molinari when asked after his round today what it would be like to become European No 1.
"I don't know how many chances you get in a lifetime, in a career, to achieve something like that.
'It would be great. Obviously it's not really so much in my hands now. I need to go out tomorrow and try to shoot 8-, 9-, 10-under if possible, and if not, just sit down and see what happens."