Into his third season at United, Van de Beek is no closer to holding down a regular first-team spot, having played just 19 minutes of Premier League football this term after spending the latter half of last season on loan at Everton.
The 25-year-old was handed his first start of the season in the Europa League against Real Sociedad on Thursday night, but was ineffective as United stuttered to a 1-0 win.
"He had a good preseason and then got injured, now he is back," Ten Hag said in a news conference ahead of United's clash with Aston Villa on Sunday.
"I think it was a decent performance [against Sociedad] but he can do better. I know him very well [from Ajax].
"He delivered what I expected in terms of positioning, pressing and in the transition. I can only talk about him [at United] from my time here and I think he can do more."
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Two players who are back in the United first team after being left out earlier in the season are England defenders Harry Maguire and Luke Shaw, with Ten Hag highlighting how the timing could be useful ahead of this month's World Cup in Qatar.
"England definitely have a really good chance to win the World Cup because they have a really strong squad," he said.
"I have to look after Manchester United, but they have to be one of the tournament favourites for sure."