Manchester City had ample opportunities to win this tie by more than just the one goal but did not have the cutting edge in the final third.
Birmingham’s steely back line played a part as they tried to close down the spaces and make it tricky for the visitors to play it through the defence, but they should really have scored more.
They managed 15 shots but hit the target with only four as they generated 1.67 expected goals.
Jeglertz’s side hit the woodwork three times, with Shaw the first to do so at 1-0 as a fierce strike cannoned off the bar after hitting defender Neve Herron.
Yui Hasegawa sent a powerful effort towards the target, but goalkeeper Lucy Thomas managed to push it on to the bar.
Even set-pieces, which have often resulted in goals for the Women’s Super League side this term, could not deliver their second as Rebecca Knaak crashed a header off the bar from a late corner.
As with Charlton making it difficult for Liverpool on Saturday, Birmingham proved they were capable of dealing with top-flight opposition.
They are currently top of the WSL 2 on goal difference and have a game against second-placed Charlton left to play.
However, they could not punish the visitors for lapses at the back despite having some nice moves, managing just two shots and hitting the target with neither.
While this was not the display the visitors’ supporters would have been hoping for, Manchester City showed their professionalism as they defended their advantage and managed to prevent being knocked out.
Victory also keeps alive their hopes of achiving a league and cup double, currently sitting nine points clear at the top of the WSL.
