Jess Park's early goal was enough to earn Man Utd a first win in three games but not sufficient to avoid the Women's Champions League knock-out play-offs despite a 1-0 victory over Juventus in Turin.
Skinner's side had to battle back from 3-0 down to claim a point against Tottenham on Sunday after shipping another three against Lyon in the Champions League last week, which had left automatic qualification out of their hands going into the final round of fixtures.
A trip to Juventus looked an imposing opponent to mount any such recovery with the Italians having lost only once in the group phase coming into the game, and they could have led early on but for a fine Phallon Tullis-Joyce stop from Amalie Vangsgaard after she had robbed Maya Le Tissier.
But once Park had curled in a beauty to put the visitors ahead, they began going through the gears. Melvine Malard's powerful effort was turned around the post by Pauline Peyraud-Magnin while Park looked determined to add to the scoreline herself with a number of near misses and blocked shots.
Man Utd's main worry was the manner of their scoreline with Skinner opting to wait until the final 15 minutes to make changes given his thin squad, but with his side more compact and organised than they have been for some time, their lead was rarely in real danger.
They should have had a chance to relieve any pressure in the final minutes when Elisabeth Terland was clearly caught by Cecilia Salvai in her own box, but both the referee and VAR saw nothing untoward.
Eventually it did not matter, as Man Utd saw out a victory which sees them seeded in Thursday's play-off draw, and facing either Atletico Madrid or OH Leuven for a place in the quarter-finals.