United, who began the season under David Moyes, need to beat Southampton and hope Tottenham lose to Aston Villa if they are to finish sixth and qualify for the Europa League on the final day of the season, having suffered 12 Premier League defeats.
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"It's been a disappointing season but just like being players if you have setbacks, if you are a proper player you come back,” he said at United's end of season awards. “If you are a proper team and a proper club, which we are, you always bounce back.
“In my first season we lost out to Leeds and I was sitting in the changing rooms there watching grown men cry.
“I saw how much it meant to people but we came back the next year and won the league for the first time in 25 years. That's what great clubs do. They have setbacks but they come back stronger.”
David De Gea won both the Players' Player of the Year and the Fans' Player of the Year at the ceremony, while Giggs was honoured with a Lifetime Achievement award.