Southampton suffered a set back as they try to escape the League 1 relegation zone.
After two fine cup wins it was down to earth with a bump as Poyet's Brighton took all three points at St Marys.
Glenn Murray scored twice for Brighton iside 5 first half minutes before Rickie Lambert pulled one back from the penalty spot to make it 2 - 1 at half time.
But instated of a Saints fightback Andrew Crofts scored a third for Brighton to give Poyet a winning start to his Brighton career.