Sam Allardyce’s well-drilled side recovered from Sadio Mane’s early opener for the hosts to nick a point thanks to Semi Ajayi’s equaliser eight minutes from time.
Liverpool missed the chance to go five points clear at the top of the table, instead staying three points ahead of Merseyside rivals Everton in second place.
Klopp was impressed with how West Brom carried out their defensive tasks as Liverpool failed to win at home in the league for the first time this season.
"It was our own fault. I don't think anyone can expect that a team plays like West Brom in the first half, like a 6-4 [formation] or whatever it was," Klopp told Sky Sports when reflecting upon Albion's ultra-defensive approach before the break.
"I thought we did okay. We scored the goal and didn’t give anything away, especially no set pieces.
"Second half we didn't do the same again. Already in the first five minutes of the second half they had like three counter attacks. We gave them easy, simple corners.
"It was the only thing that they wanted to have and we gave it away. That's why it's our fault and that's why it is only one point instead of three."
"It is an incredible challenge to stay active and lively when you constantly face 10 men," added Klopp, whose team dropped points from a winning position at Anfield against a side starting the day in the relegation zone for the first time since December 2016.
"To be fair, West Brom did their job exactly for 90 minutes. West Brom deserved the point because we didn't finish the game, we didn’t have enough clear-cut chances
"It is difficult to create. It's a busy period, all that stuff, it's all an explanation. In the end, everyone knows and feels we should have and could have done better.
"In the second half we played around, crossed the ball and instead of moving we didn't switch. It is not a game we will talk about in 20 years but it is a game we had to play and we didn't play as we could."
Liverpool are away to Newcastle United in their next league game on Wednesday.
