Sterling was jeered by some supporters, while others shouted "Stay, Raheem" as he picked up the accolade a day after British media reported that the 20-year-old was poised to request a transfer.
In February, Liverpool manager Brendan Rodgers said that Sterling had been offered an "incredible" new contract, with some reports suggesting the club had put forward a deal worth 100,000 pounds per week.
Sterling denied he was a "money-grabbing 20-year-old" in an interview with the BBC last month but also said he was in no rush to sign a new contract.
Liverpool, who finished as Premier League runners-up last season, have struggled throughout the current campaign and have failed to qualify for the Champions League.
Speaking at the club's awards ceremony, Rodgers said this season has been a struggle for fifth-placed Liverpool because of a number of "distractions".
"Expectancy from last season was going to be high," Rodgers said. "Things that have happened, the distractions, you can't plan for them.
"It has been a difficult, trying season but the players will all be better for it next year.
"The players need a rest but the club will continue to work hard to improve the squad and next year provides another great opportunity for us like last season."
Liverpool travel to Stoke City for their final Premier League match of the season on Sunday.
(Reporting By Michael Hann; Editing by John O'Brien)
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