Chelsea paid their worthy opponents several tributes long before Mourinho revealed the secrets of his dressing room, adding: "Everton are a very tough, good side. They made it very difficult for us and our goal came at just the right time."
He was right. The 15-minute spell that preceded Arjen Robben's 72nd-minute winner saw Everton at their organised and inventive best, Mourinho's initial attacking substitution failing to give Chelsea the edge while the visitors began to play with a swagger and belief that could, and should, have seen them strike first.
After the breakthrough came the compliments. Mourinho withdrew two forwards, Eidur Gud-johnsen and Damien Duff, for the defensive Geremi and Robert Huth and for the final 10 minutes Chelsea were content, anxious even, to get to the corner flags and play out time.
Not that backhanded praise eased the pain of defeat among Moyes and his players afterwards of course.
If there was an obvious difference between the sides on Saturday it was the unfortunate reminder that while Everton do have a quality unit they cannot afford explosive individual talents who can polish bright performances with that decisive touch.
And while the title race is still in its infancy they have the ruthlessness and feel of a championship winning team already.
"If we had £12m to spend on one player then we'd have bought Robben. But if you can't afford Armani then you have to shop in Marks and Spencer's," was Moyes's honest assessment. Not that he has any cause to complain about his own version of M&S or offered any.
His side took the game to Chelsea from the first whistle, Steve Watson breaking free inside the area within 20 seconds and claiming a penalty for handball when his low shot struck the diving John Terry.
And in an absorbing game of few clear-cut opportunities it was Everton who created the finest and rued their failure to take any.
Tim Cahill was first to provoke Moyes into head-in-the-hands exasperation on the touchline on 17 minutes when he ghosted onto the lively Kevin Kilbane's cross from the left and found himself with a free header at Petr Cech's goal.
The Australian international connected cleanly but without the accuracy of Manchester City and Portsmouth he allowed Cech to clear at full stretch and the first golden opportunity had gone.