Scott Rogers' charges gave a good account of themselves, but the Londoners carried more clinical threat in the final third.
In bitterly cold conditions, the tie at Prescot Cables FC went ahead following a morning pitch inspection.
Rogers was still without the servies of influential captain Gemma Bonner while loaneed and leading scorer Bethany England couldn't play against her parent club.
Liverpool started brightly with Laura Coombs and Caroline Weir seeing plenty of the ball in midfield. A superb pass from Weir almost put Martha Harris through on goal, but she was blocked out well by the covering Millie Bright.