For 86 minutes, he was proven right. By the end, it was their opponents believing that good things come to those who wait.
Related ArticlesMarouane Fellaini out for rest of seasonEuropa League tablesEuropa League fixturesMoyes: Sporting clash 'cannot be typical British game'Moyes: play-off for fourth Champions League spot flawedSport on televisionEverton had produced a display of the requisite maturity, keeping their heads, prizing the clean sheet above all, as Europe commands that teams should, and seemed to be set fair to put one foot into the Europa League's last 16.
Sporting, their Portuguese guests, looked technically accomplished, sure in possession and boasting plenty of craft and guile in midfield, but offered little threat.
The hosts had opened the scoring thanks to Steven Pienaar after 35 minutes, teed up in the most delicate fashion by Tim Cahill's wonderfully inventive backheel, and Sylvain Distin had doubled their advantage from a Leighton Baines corner after the break.
On the sidelines, the Scot would have been quietly satisfied. True, the lead could have been greater, had Rui Patricio's reflexes not held in the early stages, first to deny Louis Saha and then, as he scrambled from the ground, Leon Osman.
Saha, a thorn in Sporting's side all night, had headed over from another Baines free kick when well placed, while the French striker had just been an inch short of collecting a Yakubu backheel, almost a mirror image of Cahill's sleight of foot for the opener, to put the tie beyond doubt.
But there remains doubt in Everton's minds where Europe is concerned.
Gradually, they allowed their visitors territory, and possession, and supremacy. Sporting needed no second invitation. Liedson robbed the dawdling Sylvain Distin, raced away from the Frenchman and duped him into a trip.
Penalty, red card, and a Miguel Veloso away goal, the very thing Moyes had hoped patience would avert.