Virgil van Dijk headed the Reds in front at the Bank of America Stadium before the break and they had the better of the early exchanges when the action continued.
But as tiredness set in, the Bundesliga side levelled through a Christian Pulisic penalty midway through the second period.
The USA forward then put his team ahead one minute from time with a low finish and it was his strike that was parried into the path of Jacob Bruun Larsen for BVB’s third.
After the conclusion of the International Champions Cup clash, Klopp reflected on the performance and result, as well as the individual displays of Naby Keita and Daniel Sturridge.