The Reds suffered a second loss in as many games during their tour of the United States so far after Alejandro Pozo struck in the 90th minute in Boston.
Earlier, Divock Origi had cancelled out an opener from Nolito in the first half and Sevilla were reduced to 10 men when Joris Gnagnon saw red for a rash challenge on Yasser Larouci with a quarter of an hour left to play.
Afterwards, Klopp addressed the media at Fenway Park in his post-match press conference and explained that although disappointed by the reversal, he believes it will ultimately prove a useful reference point in planning for the new campaign.