But a prospective comeback was well and truly kickstarted when a brilliant cut-back from Annabel Blanchard found Haines in space, the midfielder rocketing a finish into the bottom corner against her former club.
Five minutes later, it seemed on, Johnson picking out Sharpe with a pinpoint pass over the top which Sharpe duly dinked over the onrushing goalkeeper.
As we returned after half-time, the game became end-to-end, with no side clearly on top.
Sharpe seemed to be on track to score again but Birmingham intercepted the ball in its tracks towards the goal, while Kirsten Reilly was on hand early in the second-half to produce a timely sliding tackle and clear.
The Eagles began to take control of the half, with Filbey having an effort from distance which narrowly sailed over the bar.
But the next goal went to Birmingham, Walker teed up by McLoughlin and hammering in a finish inside the box.
That strike seemed to take the wind out of Palace's sails, and Birmingham held on to see out the three points.
The defeat was, however, one in which the Eagles did themselves proud in terms of their hard work and energy - qualities they will hope to bring into their final home game of the season against Lewes Women on Sunday.
Palace: Kitching (GK), Reilly, Everett, Johnson (C), Olding, Filbey (Guyatt 84’) , Haines, Sharpe (Bailey-Gayle 85’), Hughes, Blanchard, Doran (Gibbons 73’), Hughes (Dean 73’)
Subs not used: Negri (GK), Arthur
Birmingham: Thomas, Scott, Quinn (C), Lawley, Harris, Finn, McLoughlin (Estcourt 76’), Devlin (Hodson 63’), L. Quinn (Bourne 84’), Walker (Smith 76’), Pennock
Subs not used: Jones, Simkin, Jenner, Cowie, Worsey