Ukrainian Kucher won in a brutal first round at London's York Hall.
Swansea-born Maccarinelli hoped to return to the world title scene with victory, but was floored when his opponent followed a strong left hand with a right, left combination.
Trainer Gary Lockett threw in the towel as the referee ended the fight.
Maccarinelli's defeat signalled the end of his 17-year career as a professional.
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Former WBO world champion Enzo Maccarinelli has quit boxing after Dmytro Kucher knocked him out in their EBU European cruiserweight title bout.