Van Aanholt tweeted: "Why we kneel..." with a photo of the racist messages he received on Instagram after the goalless draw at Selhurst Park, where he saw a close range effort saved by United goalkeeper Dean Henderson in the 90th minute.
Players in the Premier League have been taking a knee before matches since July, initially in support of the "Black Lives Matter" movement before the Premier League and English Football League linked the gesture to their own anti-racism campaigns.
Manchester United trio Axel Tuanzebe, Marcus Rashford and Anthony Martial, Chelsea's Reece James, West Bromwich Albion's Romaine Sawyers, Southampton's Alex Jankewitz and Arsenal's Willian and Eddie Nketiah have all been victims of online racist abuse in recent months.
The increase in online abuse of players has prompted English soccer bodies to put pressure on social media companies to tackle the problem.
Instagram has announced measures to deal with online abuse, including removing accounts of people who send abusive messages, and developing new controls to help reduce the abuse people see.