In what was a cagey affair throughout at Walsall's Banks's Stadium, Ella Toone was presented with an early chance to break the deadlock, with Villa keeper Sian Rogers forced to deny her.
Martha Thomas was then gifted with a golden opportunity of her own at the beginning of the second 45 minutes, with her right-footed effort going agonisingly close, after Leah Galton had done brilliantly to square for the Scotland international.
While City have three games left to play, the Reds only have two - the first of these is next weekend's home clash with West Ham United.