They face the long trip to Bath to face Larkhall Athletic in round three, who currently sit top of Premier Division of the South-West Women's League.
The ladies warmed-up for the Women's FA Cup with a match-up against higher-level opposition in their first match of the FA Women's Premier League Cup on Sunday.
Manager Karen Hills was delighted with the performance against Premier League National Division side Barnet.
However, despite the display, they still suffered a 3-0 defeat.
"I was a little disappointed with the result as I don't think it reflected the game," she said.
"We worked hard but we couldn't finish. That will have to change at Larkhall because we'll need to score goals to stay in the competition."
Women's Premier Leaguer Cup, Group Two
Spurs Ladies 0-3 Barnet
The result was somewhat harsh on Spurs as they could have been in control before Barnet opened the scoring.
Bianca Baptiste and Sam Pittuck combined well for the first opportunity inside two minutes but Sam slid her one-on-one chance wide.
Jenna Schillaci and Kirsten Thomson delivered a number of fine crosses from the flanks and Bianca went close again as it stayed 0-0.
Barnet forged ahead through Danielle Murphy on 38 minutes and it stayed 1-0 at half-time.
The second half followed a similar pattern with Spurs quickly out of the blocks and Sam was denied at point-blank range by goalkeeper Renata Inniss.
Jess Cheeseman and Wendy Martin worked tirelessly in midfield but the team was hit by the key second goal when Cheryl Williams curled home a free-kick.
The same played then benefited from a deflected shot that gave goalkeeper Jo Ayre no chance.
"We worked so hard but couldn't find a finish, and that was our problem," said Karen.
"If we'd have scored one of the chances at the start of either half it might have been a different game but we didn't take our chances and in games like that you have to put them away."
Spurs Ladies: Jo Ayre, Miranda Hall, Vicky Elcome, Robin Downie, Hannah Jaadla, Jess Cheeseman (Robin McEvoy, 68), Wendy Martin, Jenna Schillaci, Kirsty Thomson, Bianca Baptiste, Sam Pittuck (Ebony Heath, 82). Unused sub: Ryah Vyse.