The Netherlands international was an unused substitute as the Red Devils secured a 3-0 win at Everton on Saturday to return to winning ways in the Premier League.
Depay has managed to score just one Premier League goal in eight top-flight games so far this term.
And Van Gaal admits that it is up to Depay to prove himself and show that he will not go the way of the likes of Angel Di Maria and Radamel Falcao, who both flopped at Old Trafford.
Speaking at his post-match news conference at Goodison Park, Van Gaal said:”Ryan [Giggs] has already given advice to him but the player is responsible for his own deeds.
“You have to give respect to your team philosophy. We have seen that some players cannot adapt to the team philosophy. You cannot know in advance before you buy them.
“You have to wait and see. That happened with Angel di Maria and Falcao.”
Depay has scored three goals in the Champions League this season, including two strikes in the play-off round against Club Brugge.
United take on CSKA Moscow in the Champions League on Wednesday night.
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