As Moyes was answering some awkward questions about whether the latest set-back was a new low in an already disappointing season, Robin van Persie was telling a Dutch television station he's not comfortable playing in the United manager's system.
And Van Persie's quotes, reported by the Manchester Evening News, will have been the last thing Moyes wanted to read when he woke up on Wednesday morning:
My team-mates are in some of the areas where I want to play.
This makes it difficult for me. Then I have to change my tactics to suit my team-mates and play outside my zone.
It will not make pleasant reading for Moyes because the dressing room, for a football club, is like the Alamo.
If the dressing room—the collective term for the group of players—remains intact, with everyone pulling in the same direction, then all is not lost, regardless of how dire the situation seems.
But once the Alamo has been stormed and the dressing room becomes infected with unhappiness and dissent, the battle is as good as lost.
Sir Alex Ferguson became a master at instilling an "us against the world" mentality in his players, never mind how bad things got. And even under Fergie the Great, things occasionally got bad.
Still, he rarely, if ever, faced criticism from inside the club.
Because of that, some will view Van Persie's comments as the first signs that the wheels are starting to come off for Moyes.
Public opinion won't force the Glazers to act. Not even short-term results will—even ones as bad as the defeat in Greece.
But if the board start to believe Moyes has lost the dressing room then his days at Old Trafford are numbered.
Van Persie airing his grievances in public—comments that essentially amounted to saying the team is being set up in the wrong way—is more damaging to Moyes than any bad result or poorly thought-out signing.
It is also significant that it was Van Persie who said it.
At 30 years old he is one of United's senior players, an influential personality behind the scenes who could lead by example if he chose to.
He did it as captain of Arsenal, and without the armband at United last season.
It is right that the players should be disappointed after such a chastening night. But they need to present a united front in public if they hope to dig themselves out of this latest mess.
Van Persie's remarks were the first instance, but if senior players keep criticising the team and the manager in public then there's no point carrying on.
And United can begin the search for a new manager now.