Substitute Andy Dodds came off the bench to give United the lead on his debut but newly-promoted Taunton hit back to win 2-1 with goals in the 85th and 87th minutes.
Reds boss Rod Brown completed the signing of Naveed Adshad this week but the pursuit of former QPR hitman Dennis Bailey proved unsuccessful with the forward, released by Halesowen Town, joining Stafford Rangers.
Redditch were set to visit Cinderford Town last night (Tuesday) before a trip to Wales to face Merthyr Tydfil on Saturday (ko 3pm).
And Cowley will face his former teammates at the Valley on bank holiday Monday when United entertain Stourport Swifts in a charged Worcestershire derby (ko 3pm).
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