Both teams swapped out several players to begin the second half which brought the German side to life.
The reds only arrived in the United States 36 hours ahead of kick off and Klopp suggested the conditions caught some of the players out.
"It's not the same injury". "It's another muscle - it looks like, hopefully, only a little tear".
Set-pieces were probably the most positive thing today. It's not cool. Things like this can happen, but you don't want them to. "I'm talking about him like so many other goalkeepers", the former Spain No. 1 wrote on Twitter.
He made his return to action in Liverpool's 0-0 friendly against Bury on July 14 and then started in the 2-0 win over Blackburn.
Andrew Robertson's cross from a short corner was met with a towering header from Van Dijk that left Marwin Hitz in the Dortmund goal with no chance.
After rickets against Chester FC and Tranmere Rovers in previous outings, Karius took his cack-handed sideshow global over the weekend as the Reds took on Borussia Dortmund in Charlotte, North Carolina. We have to learn off it and go again.
Jurgen Klopp pictured on the sidelines at the Bank of America Stadium.
There are also doubts over Belgium worldwide Simon Mignolet's future but Karius feels let down by Liverpool over the expensive addition of Alisson and appears likely to be the one who leaves.
Liverpool will fly to NY on Tuesday morning ahead of their second International Champions Cup game, when they will face Manchester City the following day.