City took the lead through a fine Filippa Angeldahl finish before Liverpool hit back with goals either side of half-time.
But Jess Park drew us level before substitute Chloe Kelly bagged a phenomenal brace to regain our lead.
A late Mia Enderby strike proved to be just a consolation goal as City held out for a second successive away win in the competition following a 2-1 away victory over Everton last month.
And the boss expressed how important it was to return to winning ways on the road following a narrow 2-1 away defeat to Arsenal last week.
“Full credit to the girls, we made a lot of changes tonight and at times we showed our class,” said Taylor.
“Like I say there are little bits we need to improve on for sure but [we deserve] great credit.
“We’ve come from two away games in the Conti Cup and to take six points is really impressive.”
Watch Gareth Taylor‘s full post-match interview via the video above!