Daiki Sugioka's first-half effort proved the difference at Saitama Stadium as Bellmare held on for their first ever League Cup triumph.
Postecoglou was left to rue a sluggish first half from Yokohama and while the Tricolore improved significantly in the second half, they were ultimately unable to conjure up a response.
With four games remaining in the J. League season and safety not yet secured, Postecoglou's focus will now shift towards next Saturday's clash with third-placed FC Tokyo.
