Everton were typically Jekyll and Hyde at the Stadium of Light on Monday, producing an excellent first half an hour and through Illman Ndiaye scoring a superb opening goal, only to waste a great chance to go two up and probably win the game.
So, predictably, Sunderland took advantage, and the hosts were able to come back strongly and dominate the remainder of the match after equalising and nearly adding a few more themselves.
As well as missing a great opportunity to bounce back to winning ways after the loss to Spurs in the previous game, the Toffees may also have a new injury worry, one which they can ill afford.
Goalscorer Ndiaye limped off in the second half with an apparent leg injury, and while the extent of his problem is still unclear, he may not be fit to face the Cottagers on Saturday.
Losing Ndiaye would be a huge blow as the Senegal star has been arguably Everton's best performer so far this season.
It will also deprive Moyes of his leading Premier League scorer, and given the dreadful paucity of goals from other sources, most of all his strikers, that is a massive problem.
The lack of goals from the two centre-forwards who have cost the Blues around £50 million odd in combined transfer fees is the biggest ongoing issue threatening to undermine the team's season.
Given their performances against the Black Cats on Monday night, neither has offered any evidence that they can step up and replace Ndiaye's threat.
If the Senegal international is unable to recover in time for the Fulham match, then one attacking player who could logically replace him in the lineup is another high-profile and expensive signing: Tyler Dibling.
Despite having made such a huge effort to prise the 19-year-old starlet from Southampton this summer, the Everton manager has so far shown little willingness to give him much time on the pitch to show supporters what all the fuss was about.
Strangely, when Ndiaye went off, he was replaced not by Dibling but by Dwight McNeil instead. This was an odd decision and one that does not bode well for the youngster being given his chance.
But surely this weekend's game would represent an excellent chance for Dibling to start paying back some of that big fee, as the Toffees need to bounce back with a win before the next international break.
The question is will Moyes puts his faith and trust in the England youth international or revert to an approach he often used in the past and stick with a tried and tested option, even if that is a less dynamic and progressive one.