A repeat of the victory Neil Lennon's side chalked up against the same opponents a fortnight ago would have put them second in Group H. They hopes of qualification instead took a dent, though: Celtic were poor from the start in Amsterdam, with Dutchman Van Dijk and his defensive colleagues needing to fend of numerous attacks before Lasse Schone broke the deadlock with a wonderfully crafted goal in the 51st minute.
Celtic pushed for an equaliser with Anthony Stokes and James Forrest impressing, but were unable to find a way through.
"It is very frustrating, of course," Van Dijk told Sky Sports.
"We played very bad before the goal – I don't know what it was, it wasn't good enough.
"But after the goal we showed what we are capable of and created chances.
"Before the goal was not good enough. Maybe some players were nervous, I don't know what to say. After the goal was a good performance."
Celtic are now bottom of Group H with three points from four matches and they will need to beat Milan in Glasgow later this month to finish as one of the group's top two.
On his team's qualification prospects, Van Dijk added: "There's still a chance so it's not over but we have to step our game up and go through the next games."