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.
Manchester United boss Marc Skinner said his side are creating history after sealing a favourable draw in the Champions League play-offs.
United will learn who they face in a two-legged play-off when the draw is made at 12pm on Thursday.
Skinner told Disney Plus: "I'm really, really happy considering some of the teams we've played and some of the teams that have finished in the top six.
"There's an incredible history in this sport in the Champions League and we haven't got that. So we're creating that and to do that and finish sixth is…I've not taken it in yet.
"But I know I'll sit on the plane home and be really proud of everyone involved in all the things we're trying to achieve."
England forward Park said United had taken a "really big step" after clinching victory for her side in their final group game with a neat curling effort from just inside the penalty area in the 18th minute.
She told Disney Plus: "It was an incredible moment. I really enjoyed it. A good finish as well, which I was proud of.
"All the girls fought and I'm proud of the whole team. We've made history as a team. We've done it together. We've made a really big step."
The Women's Champions League league phase is over!
Chelsea secured a top-four finish, meaning they go straight to the quarter-finals.
Arsenal and Man Utd finish fifth and sixth respectively. They will be in the play-off round in February and one will face Atletico Madrid, while the other will meet OH Leuven.
They will find out their respective opponents in the draw on Thursday (12pm).
One thing we do know is that if both Arsenal and Man Utd reach the last eight, one of them will face a huge all-WSL showdown with Chelsea. What an occasion that would be!
