Sadio Mane and Philippe Coutinho scored to put Liverpool on course for a fifth league win in six matches, before Gareth McAuley pulled one back from a corner in the 81st minute to set up a frenetic finish.
The Reds managed to hold on to their lead and move level on points with Premier League leaders Manchester City.
Despite keeping only one clean sheet in their nine league fixtures so far, Klopp dismissed the assertion that the Reds were fragile at the back.
"I heard it a few times [that Liverpool are suspect defensively] but I lose respect when people say this," the 49-year-old German was quoted as saying by the Liverpool Echo.
"That's not important because I do not have to respect everybody and I don't need most of the people.
"I'm the coach of this team, I'm really close to them. I see all the games from quite a good perspective.
"We defended well against [Manchester] United, brilliant, and then against West Brom it was so difficult but we have no defensive problem.
"We needed to be really aggressive to defend their long balls from the first moment without making fouls. That's quite a challenge but they did brilliantly.
"When the ball is in the air, [Salomon] Rondon wants the ball or a foul, so Dejan [Lovren] and Joel [Matip] were outstanding."
West Brom boss Tony Pulis said Liverpool had a "free run" at the league title this season because they were not playing in Europe, but Klopp dismissed the notion that the lack of midweek European football was an advantage.
"I played in Europe before and it never stopped us actually doing what we had to do," he said.
"Playing good football is a big advantage, having good players is a big advantage. Not playing in the week can be a big advantage when you take injury worries out of it. You need to use the extra time for training."