The England international notched five goals and two assists in the month of February while the West Ham boss guided his side to four consecutive victories
Sturridge notched five goals and two assists in February as Liverpool claimed three wins from four matches, including a 5-1 destruction of Arsenal at Anfield.
The 24-year-old scored in that match, also netting away from home against West Brom, Fulham and twice against Swansea City.
Those goals have helped Brendan Rodgers' men maintain their first Premier League title challenge for five years - they currently lie second, seven points behind leaders Chelsea with a game in hand.
Allardyce has been recognised as February's best manager after guiding his side to four consecutive victories and easing their relegation fears.
West Ham defeated Swansea City, Aston Villa, Norwich City and Southampton in a month which saw them rise as high as 10th in the Premier League.
They remain in the top half with 10 matches to go in the season, a healthy six points clear of 18th-placed Cardiff City despite having played a game less.