Casey Stoney said her dressing-room message before a stunning 2-0 defeat of Manchester City in the Continental League Cup – the visitors’ first in domestic competition this season – was: “You belong at this level, you’ve got to start believing it.”

“And that was my message at the end of the game,” the Manchester United manager added. “‘Do you believe it now?’”

Stoney knew what United had to do, her team having dominated the first half of their opening-day defeat by a patient City in the WSL. That had given United the blueprint. “I’m sure Nick [Cushing, City’s manager] will say City weren’t at their best today but I think we stopped them from being at their best,” Stoney said. “The first 45 minutes against City at the Etihad were key because that gave us the belief that we could compete.”

Whereas in that fixture United were not clinical enough, here they were. With the home side targeting City’s right full-back Gemma Bonner, drafted in to replace Aoife Mannion, who ruptured an ACL in the draw against Atlético Madrid on Wednesday in the Champions League, they had an almost instant impact.

Jess Sigsworth slides home Manchester United’s second goal against City. Photograph: Magi Haroun/Rex/Shutterstock

With Leah Galton, arguably United’s player of the season, receiving a long ball over the top of her wide on the left she and Bonner went shoulder to shoulder. The defender got a touch but could only play it back into the path of Galton, who powered into the box and cracked a shot which ricocheted off several City players. Hayley Ladd collected the loose ball but was scythed down on the edge of the box. It could have been a penalty but it did not matter because up stepped the captain, Katie Zelem, to score from the free-kick.

She hit a looping, powerful shot into the far left corner past the fingertips of a diving Ellie Roebuck. “I’ll just try to be the best person I can be and the best captain I can be,” said the No 10 when asked if being a fan makes the badge and armband weigh more heavily.

With both sides pressing hard, United continued to have success on the left, exploiting the gap between Bonner and the Canadian forward Janine Beckie. Stoney urged Galton to drop in and take advantage but Cushing pushed Jill Scott over to fill the hole.

With that avenue closed off in the second half, United switched their focus to the right. Jackie Groenen and Kirsty Hanson linked seamlessly to give Demi Stokes the slip before Hanson whipped a cross to the feet of Jess Sigsworth, who poked in from close range.

Keira Walsh is given a consoling pat by Manchester City’s manager Nick Cushing after being sent off against Manchester United. Photograph: Magi Haroun/Rex/Shutterstock

City frustrations told in the 65th minute when Keira Walsh’s mistimed tackle on Hanson earned a red card, ruling her out of the game with Arsenal next Sunday. Cushing had no complaints. “It was a strong tackle. I know Keira well and I don’t think she went in intentionally to try and get the girl. In the modern game you can’t go in out of control.”

City visit the WSL champions before they travel to Madrid for the return leg of their Champions League last-16 tie and, having lost and conceded goals in domestic competition for the first time this season, they will have to dust themselves off quickly.

“I don’t see it as my job to pick them up,” said Cushing. “I see it as their job to pick themselves up. Look, if a defeat against Manchester United in a local derby doesn’t kick you up the arse then nothing will. When you’re a winning team it hurts because you don’t lose that often but you have to use that as fuel.”

For Stoney, this win gives the United team belief in her strategy. “They sit in that changing room and their shoulders are a little bit higher, their chests are out a little bit more, they’ve got more belief in their psychology and they trust what we’re doing as staff now to deliver that gameplan, which they executed brilliantly.”