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James Rodriguez bagged a brace for the Baggies and Joel Matip put through his own net.
Roberto Firmino scored Liverpool’s opener - but missed a penalty later in the first half.
Prolific Egypt international Mohamed Salah also got on the score sheet as he continues an impressive run of form.
Klopp, however, is adamant that his expensively assembled squad simply weren’t good enough.
"It's obvious what we did wrong in these situations," he said.
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“It's obvious what we did wrong in these situations”
Jurgen Klopp
"The second goal was just, wow, really bad defending from the whole group. That's not how defending should be.
"We didn't use the chance on the penalty and then their third goal must be off-side. 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 have only ourselves to blame."