Italian striker Pelle, who joined the club from Feyenoord last summer, edged out team-mate Morgan Schneiderlin to the accolade after netting three goals - including a spectacular overhead-kick winner against QPR.
Koeman guided the third-placed Saints to three wins out of three last month, beating Newcastle United, Swansea City and The R's.
The Dutchman faced stern competition from Leicester City boss Nigel Pearson, Chelsea's Jose Mourinho and Neil Warnock of Crystal Palace.