The 19-year-old, who signed a contract extension at Spurs last week until 2021, appeared to intentionally throw the ball into Van Aanholt's face during Saturday's 4-1 Premier League victory over the Black Cats.
Alli has been a key player for Spurs this season, having scored six times in 28 appearances in all competitions, and he made his England debut last year.
"I didn't see it, this is the truth. He's very young, he needs to learn a lot. It's a little bit naughty... I like how he is because you need to be a little bit naughty when you play football," Pochettino told British media.
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"He's young and we need to accept that he needs to learn in a professional side. Sometimes you need to be hard with him, sometimes you need to be friendly and give love. It's like your son."
Tottenham, who are fourth in the table, travel to eighth-placed Crystal Palace on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru)
