Klopp confessed after the action-packed match that his side did not deserve to take anything from the game, however, as their defensive frailties again came to the fore.
"It's obvious what we did wrong in these situations. The second goal was just, wow, really bad defending from the whole group. That's not how defending should be," he told BT Sport.
"We didn't use the chance on the penalty and then their third goal must be offside. What can you do? We had to show character in the second half.
“We chased the game and maybe scored the second goal too late. When you start how we did you cannot play your best football game.
"They tried to save some time - which was normal - and in the end, West Brom deserve it because they scored three goals and we only scored two. They did well and fought with passion. But we only have ourselves to blame."
Watch below to hear more of the German's assessment.