The win was sealed after goalkeeper Phallon Tullis-Joyce committed a foul on Mayra Ramirez inside the box. Guro Reiten took charge of the penalty kick and coolly converted it, securing the victory for her team.
The defeat means United are no longer unbeaten in the top-flight and sit in fifth, nine points behind leaders Chelsea.
Manchester United: What have fans said?Calls from fans for Skinner's departure started towards the end of last season and have not stopped despite him winning the FA Cup with the club in May.
The sacking pleas increased in volume after Sunday's loss with some accusing Skinner being 'happy to lose' after he praised his side's performance against Chelsea.
Skinner told Sky post-match: "Chelsea are the best team in the country, they have been for years. They are champions for a reason. We came here and we said we would give everything from the off, I felt the players, you can see their reaction after the game, they've given everything.
"Both teams had to play the conditions. The pride I feel for the team and their commitment to what we're doing, what we know we can do. Even though we have taken a defeat, I'm really happy with their performance."
Get FourFourTwo Newsletter Contact me with news and offers from other Future brandsReceive email from us on behalf of our trusted partners or sponsorsBy submitting your information you agree to the Terms & Conditions and Privacy Policy and are aged 16 or over.Supporters took to social media to share their frustration with the manager.
One fan wrote: "Can't believe how happy Marc Skinner is to lose. Man United's performance was awful, they had one shot on target and just 11 touches in the box against a Chelsea side who barely had to try. Bring back shame."
Another posted: "1 shot on goal, 30% possession, 64% pass accuracy, 11% cross accuracy (1 successful), 26% long ball accuracy. How much longer can Marc Skinner be manager and this is a norm?"
While another supporter wrote: "I don’t think we’ll ever see the true potential of our players with Marc Skinner at the helm. Truthfully we all deserve better than him."
In FourFourTwo's view, if he doesn't bring silverware this season, no one would be surprised to see Skinner replaced.
The boss' contract was due to run out this past summer but the club gave Skinner a short-term contract extension. There has been no confirmation on when that runs out.
Skinner has been in charge of United since 2021 and has since delivered the FA Cup. The club also challenged Chelsea for the WSL title in the 2022/23 season but the Blues pipped them to the title by two points.