The centre-back was forced off in the 55th minute at Red Bull Arena, where Rhian Brewster struck twice in the second half for the Reds.
But Klopp confirmed post-match that Van Dijk is not expected to suffer any lasting effects.
“Virg only looks like he has a piercing now and has a plaster on it. It should not be, and is, no problem,” the manager told Liverpoolfc.com. “In the moment it is of course not cool but there will not be a problem.”