Keane questioned the performance and leadership shown by Van Dijk as Liverpool lost for a fourth consecutive time.
He told Sky Sports: "When you're a centre half and you're a big player, last year we were on about who was going to stay and he signed a big contract, then you're giving up loads of goals. I'd be looking at him and asking 'what are you doing'?
"Particularly as a big leader of the team. A couple of years ago we talked about United parking the bus here and we were critical. Now they've scored two today and two last year and you're the centre half.
"Always start with the man in the mirror. Van Dijk, if you're the centre half and your team are all of a sudden giving up loads of goals, and you've got new people coming to your club, you've got to have a good look at yourself and think 'am I really helping people?'"