Natalia Ramos' 93rd-minute goal means the Reds have two victories from two in the league phase of this season's Subway Players Cup.
Marie Höbinger put the Reds 1-0 up early on but they then found themselves 2-1 down because of Marie Levasseur and Lee Geum-min strikes either side of the break.
After the visitors established a 3-2 lead through Neve McDonald and Höbinger, Birmingham responded again with Wilma Leidhammar's long-range hit.
However, Taylor's side left St Andrew's with the points after substitute Ramos netted from a corner deep into stoppage time.
Read on for Liverpoolfc.com's post-match interview with the head coach.
* [**Subway Players Cup match report: Birmingham City 3-4 Liverpool**](https://www.liverpoolfc.com/news/stoppage-time-goal-gives-lfc-women-4-3-win-birmingham-subway-players-cup)
**On what he enjoyed from the game...**
I enjoyed seeing Maizie Trueman go onto a decent stage as a 16-year-old and not be daunted by it. I think some of the things I was a bit disappointed with was our general levels. Because we want to be this team that is really aggressive, we want to be able to really, really press and play a half-pitch practice, and the game was too open, way too open. They were playing a lot of direct balls that we weren't dealing with well and therefore we ended up doing a lot of running, which was unnecessary.
The good thing about Maizie Trueman is she's someone who can cope with the physical demands of the game at 16, which tells you a lot. And then we had some changes at half-time that helped a little bit in Kappy \[Cornelia Kapocs\] and Natalia. I get it because it's always difficult for the players who are not playing so much that they're a little rusty. But we train it every single day. We do so much training and train that physicality, train that aggressiveness and train the quality with the ball, and we were just off it a little bit tonight. So, good character in the end but lots to work on for sure.
**On Höbinger's display...**
I just said to Herbie that it's brilliant to have a No.6 that can score. She's playing into that low role but she's still got around the edge of the box and caused problems for their 'keeper. She scored a really good early goal as well and showed some nice moments. We've just got to be really conscious of where Marie's at. She came back from a difficult injury and the signs have been really good because she's actually progressing along really nicely.