Other good chances came and went as the Gunners controlled the first hour of the game, but the visitors took charge in the closing stages and the striker Natasha Harding twice missed close range opportunities to clinch victory.
The Academy manager Mark Sampson said: "We were disciplined, intelligent and in the end should have won. Arsenal won't give up the title lightly, but Liverpool and us have been competitive all season and it's going to be a fantastic finish."
As the interim manager of the England women's team, Brent Hills, prepares to name his squad for the opening World Cup qualifier next week, against Belarus at Bournemouth, the Football Association is assessing applications to take over the sacked Hope Powell's position as national coach.
The appointment will be made by Club England, the FA body that last year put Roy Hodgson in charge of the men's senior team, with the director of football, Sir Trevor Brooking, playing a key role along with other Club England officials plus Kelly Simmons, director of the national game and women's football.
The FA has reported a "high level of interest" in the position, the deadline for applications having closed on Friday, and it is hoped that the new coach will be unveiled ahead of the qualifier against Wales at Millwall next month.
Hills, who has been assistant to Powell since 2002, is believed to want the job full-time but there is a coyness from potential candidates as to whether or not they have applied.
Calls from within the women's game for the FA to approach the Newcastle-born Canada coach John Herdman, who led his team to bronze at the 2012 Olympic Games, must go unheeded following the former New Zealand manager's decision to sign a new contract that will keep him in North America until 2020.
It may be easier to wrest another Englishman, Estonia manager Keith Boanas, from his current position if the FA, as it has suggested, is prepared to consider male as well as female coaches following Powell's 15 years in charge.
"I'm sure that my employers would release me if the [England] opportunity arises," said Boanas, a Uefa Pro licence holder who has been in Estonia for five years after a successful stint as Charlton Athletic's manager.
If the FA decides to appoint from within then Under-19 coach Mo Marley, who has led England to four under-19 European Championship finals in the past seven years, should be in the running.
However, Chelsea's former Chicago Stars manager Emma Hayes, another possible for the position, said: "It should be Mo's job, but the players have been very clear about wanting a clear break from the past."
Hayes, like Boanas, will not confirm whether or not she has applied for the job.
She said: "I've always said that one day I would love to coach England, and maybe the job won't come around for another 15 years. I'm English, and I'm interested, but I'm not going to push myself."