Manchester City’s women are in their first FA Cup final where they will face Birmingham City at Wembley following this accomplished win courtesy of Melissa Lawley’s precise second-half goal.

Nick Cushing’s side lost at the semi-final stage a year ago so this win was particularly satisfying and maintains City’s bid for a treble of Super League, Cup and Champions League.

“I’m proud,” the manager said. “We want to be a winning team and the result of playing good football and entertaining the crowd is you win games. Last year we were [too] desperate to reach Wembley. Now we’ll forget Wembley – we [just] want to win the FA Cup.”

The chance to do so came before a 3,459 crowd in a match for which Cushing made one change from the XI who sealed a European Cup semi-final place, Izzy Christiansen replacing Kosovare Asllani.

Scott Rogers adjusted Liverpool from the side who knocked out Notts County in the previous round by drafting in Katie Zelem and Niamh Charles.

City dominated from the kick-off until the final whistle, causing most problems along the flanks via Christiansen and Lawley and the full-backs Lucy Bronze and Demi Stokes.

A first warning came when Keira Walsh floated in a free-kick on an enticing left‑right diagonal but no team-mate could prosper. Next, Lawley was given a clear sight of the Liverpool goal from a Bronze pass but the No14 could only hit the ball at the keeper.

Sandwiched between this action was a miskicked cross from Kate Longhurst that beat Karen Bardsley but not the City keeper’s left post. And, after a strong Shanice van de Sanden run down the right, which was ended by Walsh’s tackle, Liverpool were forced to constantly defend for the remainder of the opening 45 minutes.

Jane Ross, the striker in Cushing’s 4‑1‑4‑1, cursed her touch when in space. Then, just after the half‑hour, Casey Stoney, who has won the FA Cup four times, required treatment but was able to resume promptly. She is Liverpool’s star turn, a defender with a combined 123 caps for England and Great Britain and in the American Carli Lloyd City have their equivalent.

The double Olympic champion and World Cup-winner endured a quiet opening period in her central-midfield role and with the tie level at the break Cushing may have asked for more of the ball to be channelled through Lloyd’s playmaking abilities.

Christiansen should have affected that half-time score but was unable to find Ross five minutes before the interval, her cross from the right sprayed aimlessly to no one.

Lloyd was involved early in the second half but after a strong run along the left her ball disappointed. Again, though, by widening the contest City stretched Liverpool: a Stokes delivery begged to be finished and when Christiansen pinged the ball back in the visitors again lived dangerously.

City had increased the speed of their play. They zipped the play around all areas of the final third and so posed far more questions of the visitors.

Then came the opener – and winner – City deserved. Possession broke just outside the visitors’ D and Lawley dropped a shoulder and threaded a 20-yard shot past Chamberlain.

City’s next move featured a slick Christiansen touch, a driving pass into the area and a sweet Lloyd turn. She was unfortunate not to double the lead. From here City were in cruise control against a Liverpool side who offered very little. Cushing said: “I expected them to sit in and try to frustrate us, we had two games last year which were drew 0-0 and 1-1 and when I thought of the coach’s mind I imagine Scott thought: ‘It was pretty successful so let’s do it again.’ We spoke a lot before about being patient and I thought that’s what the team, did so I’m really pleased.

“In the three seasons I’ve been with the team we’ve not really scored a lot of goals but we do tend to dominate the ball a lot so it’s more mentality, not to get frustrated. We’ll always a find a way.”

They now hope for the same in the European Cup semi-final first leg against Lyon at the same venue on Saturday.

“It’s going to be a tough game,” Cushing said. “They’re the best team in Europe if not the best in the world in women’s football. We need that test to see where we are at. We think we’re a good team. So we’ll forget the Wembley game and start planning for Lyon.”