The Cardiff Lord Mayor, and former partner in the firm of Keane & Co, received 67 votes in the final round compared with 110 for the victor, Swansea lecturer Huw Irranca-Davies.
Earlier, Goodway led Irranca-Davies by two votes, but he lost out when the second preferences of other candidates were redistributed.
During the run-up to the contest Goodway had to be reminded of Labour’s code of conduct banning canvassing for support.
He is understood to have made it clear he issued letters stating he was thinking of standing before having reached a decision to do so.
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