Albion were beaten through goals by centre-back Dennis Lawrence after 52 minutes and the Welsh sides new signing Chris Llewellyn doubled the score on 71 minutes.
Albions best effort came through James O'Connor whose scissor-kick inside the box was well saved by Wrexham keeper Paul Whitfield.
Albion: Hoult; Wallwork, J Chambers, Gilchrist; Haas, O’Connor, Gregan, Koumas, Clement; Dobie, Hughes. Subs: Murphy, Dichio, Roberts, Johnson, A Chambers, Dyer.