The 20-year-old forward received the accolade 24 hours after it emerged that he will ask to leave to club.
But while some fans jeered, others shouted: “Stay, Raheem.”
The England international is expected to tell manager Brendan Rodgers and chief executive Ian Ayre tomorrow that he wants to leave Anfield this summer.
Speaking at the event, Rodgers said it had been a “difficult, trying season”.
Liverpool will finish outside the top four in the Premier League and therefore miss out on a place in next season’s Champions League, while Rodgers is first Reds boss to fail to win a trophy in his first three seasons since the 1950s.
He added: “A number of distractions that we couldn’t have planned for have made it difficult, but the players have given everything.”
Brazilian midfielder Philippe Coutinho, 22, was voted Player of the Season.
Sterling rejected a new £100,000-a-week contract in April but denied being a “money-grabber” in an exclusive interview with BBC Sport which was not authorised by his club.
The forward told Rodgers before Liverpool’s 1-1 draw with Chelsea on May 10 that he wanted to leave, but it is understood the Reds want to keep the player, whose deal ends in 2017.
Should Sterling be made available, Manchester City are the frontrunners for his signature, while a number of leading European clubs have also expressed an interest.
Arsenal manager Arsene Wenger refused to be drawn on whether he would make a bid.
Several former Liverpool players have criticised Sterling and his representatives. — BBC